What would cause it to occasionally lose power completely while driving at low speeds?

Check for if your belt is loose,that can cause to lose power performance ,Check also your transmission oil,If too low it can also lose power performance..Also check if you have an engine default code indicators appears on your instrument panel..in other words Check engine light....

Sounds like the idle speed of your car is too low, then the alternator cannot produce enough voltage for any electrical devices. When idle speed is normal or much higher, power will return to normal very fast. It may be that the idle air control valve is dirty or defective.

I would test coil and ignition module. Module has a low speed and a high speed section, so high speed part could be bad and cause unit to die, then start right back up on low speed part.

loses power
well if the RPM advances fast on engine and the car speed dont
that is tranny slip.
on the other hand if the engine RPM stays low, and speed is low that
is engine power loose.
2 completly different things, why not ask him which it is.
is my engine weak or is the the tranny slipping.
surely you know what slip means. right>?
like bumping in to neutral , under power. or partially
ENGINE RPM state that, going up said hill WOT
and can tell you.

If this is a deisel then it's probably some sensor malfunction. It could be one of the sensors in the exhaust system or a simple electrical fault - I have been told it can happen if even just one brake-light bulb is broken

Can you tell if the transmission comes out of overdrive or downshifts when the speed drops ?

Check spark plugs. If completely black and looks burnt, replace them

Hello, This could be an indication your A/C is low on Freon or your Power Steering pump is low on fluid. Both systems are made to increase the idle speed to make the system work better. What happens in the case of the A/C, is the A/C compressor puts a strain on the motor when it engages the electric clutch on the compressor.

The A/C is wired such that when the compressor clutch engages, the engine RPM is increased to maintain the idle speed. The controls do this automatically and when your compressor is low of Freon, there is little resistance and the engine overspeeds. You are burning up your compressor if you lose the lubricant packaged inside it. That noise you hear is a dry compressor.

Turn your A/C or Defroster off and see if the overspeed and the noise stop. The compressor will run in the Defrost cycle too! Eventually your A/C will lose more of the Freon until the low pressure switch cuts the power to the compressor completely.

Some front wheel drive cars have a boost sensor in the power steering assembly for increasing the idle speed when you are turning the steering at low speeds. If the fluid level is low, it tricks the sensor into speeding up the idle to assist steering. Like in the A/C example, you can get overspeed when the fluid levels are low.

I hope my solution is very helpful in fixing your problem. Have your Freon checked or throw in an "OIL Charge" with the proper type of oil for your compressor. Then check your Power steering.

check oil pressure sensor on strokers need a good oil pressure before they wold start and if they lose it , it would turn off the engine

The A/C compressor clutch may be bad