A few months ago my power steering pump went out in my 1996 Grand Cherokee. I replaced the pump with a reman from a national parts supplier. The first one I bought, the rear shaft seal was never installed. I returned it and put in the second reman pump. It worked great for a couple weeks, but now I’m having a problem with it. I don’t seem to have any power steering while the vehicle is at idle. It works great if I throttle it up about 100 RPM or more. I’ve tried to flush the air out of the system countless times to no avail. Any ideas? The oil level is good, and I change it regularly 
How about your drive belt? Is it a serpentine? Make sure the belt is not worn out and the tensioner is good. At idle…a lot of belts will slip like crazy.
as far as I can tell, there is no slipping. I don’t hear any squeaking, and everything else seems to be operating normally (it is a serpentine) I have noticed, though, that my A/C compressor bearings are beginning to fail. Could it possibly be that my belt is too tight?
Is your tensioner adjustable (with a bolt) or spring actuated? An adjustable tensioner can be overtightened. Have it checked along with your compressor bearings.
adjustable tensioner. When I put it on, I was lazy and used my 1/2 impact and tested the tightness by hand. I think that’s why my compressor bearings went. I just didn’t know if that would cause a power steering issue.
If you have ruled out belt slippage, then the next step is to see if the pump can actually produce the required pressure. Plumb in a high pressure gauge with a shutoff valve in series with the high pressure line. At idle close off the shutoff valve and read the pressure (keep the flow blocked only long enough to read the gauge). If the pressure does not rise to the specification (see Alldata or your Haynes or Chilton manual), you know the problem is in the pump. You could have a stuck pressure relief valve; flow control valve, or just a badly rebuilt pump.
If the shutoff pressure is okay, crank the steering wheel to the locked position and see what the pressure reads. If the pressure does not rise to the specification again, you probably have a problem with the rack.
Good luck on this. Let us know what you find.