I have Rinnai R53 tankless water heater which is about 5 year old. recently it has problem to keep water consistant warm. when I take shower , I feel water change from hot to cold antomatically. what is problem?

It only runs when there is a demand for hot
water.

Bad remote control. Bad wire to remote control. Bad PC board.
Copy following link for resources, including older service manual and error codes and rheem chat for ordering replacement motherboard for your tankless computer.
http://waterheatertimer.org/Troubleshoot-Rheem-Tankless-water-heater.html

If tankless computer is 5 years old, then compare that to your 5-year old cell phone or 5-year old laptop, and ask if the chipware still functions or can be repaired to function back to factory fresh expectation.

Later today, install tank type water heater and solve all tankless computer problems with one ez step. Have hot water for shower same day with less maintenance and fewer long-term problems and expense.
http://waterheatertimer.org/How-to-install-gas-water-heater.html

Gene
h

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

You need a product manual for your tankless computer that heats water.
Look on side of unit for label.
Then google that brand and model and add .pdf to search parameter to find possible resources.
Or try Rinnai website for a dose of promotion about how great their product is.
If unit is a few years old (age of unit accessed with serial number), there might be no manuals posted online since manufacturers often drop manuals from website after a few years, assuming most their products no longer function correctly and thus avoid available knowledge for customer to talk specifics... instead telling customer to call service tech who of course does not have manual either because he is a tech and needs one, but got hired last week to his new esteemed position and gets paid by service call not by successful repair except bonuses for recommending replacement unit.

Read the manual. Especially required maintenance, such as deliming yearly and cleaning water filter.
Note resources for maintaining tankless appear on following link except for different brand tankless computer:
http://waterheatertimer.org/Troubleshoot-Rheem-Tankless-water-heater.html#de-lime

Also scroll down page to read explanation of high temperature limit for tankless before causing irreversible problem with your computer requiring skilled technician.
Also scroll up on page to read about no error code, since cooler than normal temperatures from tankless computer can be result of common plumbing problems like defective single-handle faucet cartridge. Or power surge, since tankless are not protected from ordinary surge event like power restored after outage.

If your tankless computer is older than 5 years, then assume it will not work better than your 5-year old cell phone or 5-year old laptop, or behave better than 5 year old child. So don't assume you are doing something wrong... just assume it doesn't work despite glossy advertising brochures from tankless manufacturers claiming 20 year lifespan for tankless computers.

Install tank type heater yourself, same day and avoid computer water heaters: Ordinary plumber can fix these units easy.
http://waterheatertimer.org/How-to-install-gas-water-heater.html

Gene
h

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Bad PC board.
Bad sensor.
Don't buy a tankless because the problems can be endless.

Before blaming the tankless however.
Perform the yearly required maintenance on burner
Delime the unit.
http://waterheatertimer.org/pdf/Bosch_Descaling-heat-exchanger.pdf

Remove and clean aerators, replace low-flow shower heads with large water-wasting shower heads.

IMPORTANT check all your single-handle faucets for crossover.
Water getting cool after 15 minutes could be bad cartridge on another faucet.
http://waterheatertimer.org/Crossover.html
http://waterheatertimer.org/pdf/No-Error-Code.pdf

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

The issue is the flow sensor, if the faucets are restricted (like showers heads) then there is not enough flow to trip the sensor. This could also be related to pipe size and water pressure.

Grundfos RCP-96 has Flow range: 0 - 27.5 U.S. GPM
According to Amazon spec sheet:
http://www.amazon.com/Grundfos-RCP-96-UP515-55SFC-Recirculator-Timer/dp/B00128BJAO

Most tankless require .4 GPM to start burner and .25 GPM to maintain burner
Rinnai does not show C85e-1 so you will have to consult your manual to see minimum water flow requirement.
http://www.rinnai.us/tankless-water-heater/
Sample manual from Rainnai mentions 'minimum flow rate' several times but doesn't give specific number. Yet promotion blurb on page 1 says "Ultra operates at a lower minimum flow rate."
http://www.rinnai.us/documentation/downloads/U290-665x0200_Condensing_Manual_EN_FR_1-2010.pdf
Another rinnai manual mentions flow rate several times in troubleshoot section yet fails to define what that rate is:
http://www.rinnai.us/documentation/downloads/U287-1833_VB_Series_R75LSi_R94LSi_R98LSi_Manual_EN_FR_EN_FR.pdf

It might seem that tankless promoters are CTA by failing to mention specific flow rate numbers.
I think tankless promotion is a definite overachiever, and vague flow rate is one tiny example.
It proves the necessity of reading whole manual and asking questions before buying a tankless.
There's another factor to consider:
All performance numbers are based on new products in ideal circumstance, and not based on a 4 year old product located in your home.

Your flow rate may vary, especially over time, and especially if water in your area is not crystal clear, and you are not diligent with correct water softener and filter.
Many factors can affect flow rates: water pressure, number of elbows, clogs in the line, sediment, size of pipe, aireators, water-saving shower heads, local water conservation policies, water well pressure, MUD district pressure issues, your home located near end of a water main, etc.

Read tankless efficiency vrs water softener
http://waterheatertimer.org/Battelle_Final_Report.pdf
Image of tankless parts vrs tank parts
http://waterheatertimer.org/images/Compare-water-heater-parts.jpg
Bradford White tankless vrs tank side by side
Lime scale does not flush out of tankless
Tankless must have water conditions with less than 11 grains hardness
"Savings falls far short of a payback," 'without comparing service costs'
http://www.pmengineer.com/Articles/Cover_Story/8cf9e86f7c298010VgnVCM100000f932a8c0____
Sediment clogs tankless pressure sensor without softener.

Possible flow switch problem, debris in the filter, bypass valve issue or water sensor. These are pretty complicated little units so I suggest calling your contractor. The unit may still be under warranty!

Tankless water heaters normally take a little longer than a regular heater to provide hot water because they have to start and get warmed up. I'm guessing the heater uses a pilot light and that the short amount of hot water when you turn on the tap is hot because when the water is sitting still in the heater the heat from the pilot light is enough to get it hot. The tub faucet will get hot a lot faster than the shower because it lets a lot more water through and empties out the pipes faster than the shower. You could probably speed things up by letting the tub faucet run on completely hot for like 10-15 seconds and then turning on the shower.

where the pipes are laid out it may run along an outer wall and the cold weather is cooling the water before it gets to the shower try to track the pipe from your water heater to your shower and insulate it where it is coldest

It sounds like the Rinnai units are working correctly but you've got some plumbing problems.  Any tankless heater has a minimum water flow required to keep the burners going.  If the burners were going with very little water flowing through them to carry the heat away, the heat exchanger could overheat and fail.  The solution is generally to the electronic controls to set the desired temperature and then just use hot water.  Once you start mixing cold water in, you actually reduce the flow of hot water and the burners turn off.  If you are right near the cut off point, the burners will cycle on and off resulting in those very annoying hot-cold-hot-cold showers.  
The fact that you've got those very loud noises indicates some other sort of plumbing problem.  Hooking up two tankless units in series is much more complicated. In heavy draw situations, the second unit is asked to finish heating the water up to temperature when the first unit couldn't quite get it there. Now you're putting hot water into a heater and heating it more.  You have a lot more issues with fluctuating temperatures and pressures within the pipes which could conceivable cause these horrible noises.  Everything's got to be set up right to for things to function properly and it's easy to get something wrong.
From your description, it sounds like a better solution would have been to mount the two heaters in different places. e.g. One in the basement to serve basement and first floor faucets.  The other on the second or third floor to serve those two floors.  Since these units are direct vent (don't use inside air), they can even be mounted in a closed closet as long as the vent can get to the outside.  With this setup you avoid the complexities of a series installation and you also have a much shorter wait time (and therefore less waste) for the fixtures on the upper floors.