2004 Hyundai Elantra GT (manual)Loosing speed/power while driving

Clutch is slipping.

run the fault codes to find the sensor that is at fault

Check the fuel pressure, could be the fuel pump

It almost sounds as if the rev limiter is kicking in.

Your transmission fluid is dangerously low (tranny is dry). The pops & jerks are the transmission
internal components trying not to seize onto each other due to lack of lubrication and/or overheating.
Low transmission fluid leads not only to loss of lubrication but lots of overheating (of the tranny).
The loss of Elantra performance (speed tops out at 55), is caused by power loss due to friction inside the transmission. All your power is lost overheating the transmission (toward destruction), instead of
being transmitted through the transmission to the wheels.

The 2004 Elantra takes Hyundai SP-III Automatic Transmission Fluid, with 8.4 quarts used in a
total refill - but just 5 quarts at a fluid change. For How-to transmission fluid change instructions:

http://en.allexperts.com/q/Hyundai-Repair-815/2004-Elantra-GT-transmission.htm

www.autozone.com claims that 2004 Hyundai Elantra can take these non-Hyundai ATF's:
Lucas Semi-Synthetic Multivehicle ATF
Pennzoil Muilt Vehicle ATF
Valvoline Maxlife Dex/Merc ATF
Castrol High Mileage ATF

Check the air filter for a blockage. If you have a scanner, check to see that the TPS (throttle position sensor) is going all the way from 0% to 100% opening as you press the accelerator down all the way, while the ignition is on and the engine is not running.
Check for codes that might lead to a solution, if the above doesn't help.

2001 elantra gets 300 miles per tank of gas regular unleaded
slow to respond when accelerated 105 K original miles recently purchased
no check engine lights most parts look original engine revs up but tranny seems slow to respond?

i had the same thing with my 01 elantra. i took it in and they had to replace the gasket on the air intake manifold. cost about CD$700

If manual transmission, the clutch is slipping. Check for pedal free play (about 1 inch or so). If automatic transmission, the fluid level may be low, or the transmission needs service.

I have one other suggestion, clear all the codes and drive the car until the check engine light comes on, then rerun the test,