The 3A fuse on the white wire keeps on failing. what could the reason be?

need a meter to test circuit for damage

This is an electrical problem I'm sorry I can't help any more than that

Call service technician
Check polarity of 120 volt outlet
Call Rheem for new PC board
If the 3A glass fuse located on PC board is blowing, then something is drawing too much current or shorted on board... problem is probably bad PC board
http://waterheatertimer.org/Troubleshoot-Rheem-Tankless-water-heater.html

Gene

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

Check for small fuse on circuit board:
http://waterheatertimer.org/Troubleshoot-Rheem-Tankless-water-heater.html
Water heater circuit boards are NOT protected from surge. And reset button does not protect from surge. Nearby lightning can put out any household appliance, especially since more of these things are electronic instead of mechanical.
Install single-use whole house surge protector and replace it after each surge event instead of replacing appliances.
http://waterheatertimer.org/How-to-wire-Whole-house-surge-protector.html
The quickest solution for tankless is to replace whole thing with more reliable tank-type electric heater for $275 from local box store.

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

Copy following link for tankless troubleshoot resources:
http://waterheatertimer.org/Troubleshoot-Rheem-Tankless-water-heater.html#fuse
Tankless are not protected from surge, but there is a 3-5 amp glass fuse located on circuit board.
Check outlet with circuit analyzer, and multimeter

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

Why is it always Rheem problems?
Every water heater problem at fixya is Rheem.
And Rheem doesn't post any service manuals, like the other two big manufacturers, AO Smith-American, and Bradford White.

Rheem 2012 manual says if error 13 still displays, then contact installer or service technician. Mo Money buddy.
This is about oxygen sensor, poor combustion, bad venting, inadequate air supply, failed sensors, etc.
Get more fresh air to unit and see if that solves problem. The call service technician, and get out wallet.
Copy following link for Rheem-richmond tankless troubleshoot.
http://waterheatertimer.org/Troubleshoot-Rheem-Tankless-water-heater.html

Maintain water heater according to instructions in manual to avoid common error codes. Of course this means you have to service the unit each month, and each year, without guarantee the thing will work correctly.


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

Before calling service technican, copy following links for general troubleshoot resources and error codes, and manusls, and Rheem contact information:
http://waterheatertimer.org/Troubleshoot-Rheem-Tankless-water-heater.html
http://waterheatertimer.org/pdf/Rheem-CondensingTankless-maintenance-2012.pdf

Error IL usually means delime the unit.
http://waterheatertimer.org/pdf/Rheem-De-lime-tankless.pdf
Read your product manual for yearly/monthly maintenance schedule.
Tankless are maintenance heavy and must be delimed each year.
Deliming using white vinegar take about 1 hour, and will not restore full efficiency to unit.
Tankless have the habit of forming lime deposits inside the heat exchanger, even with softened water.
Tankless cannot be exposed to more than 11 grains hardness in water.
Don't buy a tankless next time.
Read the manual first.

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

Not for sure what your root cause was and I know it's a little late but I just suffered this same exact scenario on the same water heater. Storms came through, power went out, power came back on and the water heater keeps blowing the 3 amp fuses now. I removed all the cables and plugged them back in one at a time. When I plugged in the Fan Motor connector the fuses blew. Installed new fuses with the connector out, the Fan Motor was putting out 150 VDC through the connector port (on main control). I pulled the control from the unit and Q1 is visible blown and disintegrated on the control board. Obvious control design issue. I've ordered a new control and will put a surge protector on the heater now when the new control comes in. Very disappointed that this was not caught in controls testing within the manufacturers facility. New control is not very cheap. Half the cost of a new Heater. Hopefully the Fan Motor survived the high voltage with the fuses blowing. I'm putting this here for anyone else that suffers the same issue on this water heater or the Richmond equivalents as they use the same control.

Open following link to see general tankless wiring instructions, with amp rating and breaker size for various tankless units including Rheem
http://waterheatertimer.org/How-to-wire-Tankless-electric-water-heater.html

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

1) All tankless water heaters require voltage to operate electronic sensors and circuit board.
This is true for gas and electric tankless.

2) Check that circuit breaker is not tripped. Push circuit breaker all the way one direction and then all the way back other direction.

3) There are fuses located inside the tankless unit, so check your manual for location of each fuse.
Manual is filled with useful maintenance and troubleshooting steps.

4) Before calling service technician, open following link for troubleshoot resources including manuals, Rheem on-line chat, and useful links for maintaining tankless water heater.
http://waterheatertimer.org/Troubleshoot-Rheem-Tankless-water-heater.html

5) If you had nearby lightning strike, I don't know if your tankless is protected from surge.
I recommend whole-house surge protector for tank and tankless water heater electronics, and household circuits. Surge protection is installed in main breaker box, and is replaced after each surge event. Separate protection needed for co-ax TV satellite, co-ax surge protection can be found on some ordinary power strips.
http://waterheatertimer.org/Intermatic-trippers-and-parts.html#surge