2001 Saturn SL1 Transmission problems

[Minnesotakid1]

Hi, I have a 2001 Saturn sl1 with the L4 1.9L engine, has only 96000 miles on it and has been a good car. The other day when it was real cold I went out and started it, and let it warm up for about 10-15 min, when I tried to shift it in to Reverse there was nothing, I had forward gears but no reverse. I let it roll down the driveway and I could use forward gears but could no faster than about 30. There were no lights or warning messages on the dash. So I put it in garage and tried it again about 6 hours later and it was fine I had reverse, and could run as normal. So I ran it a few days and it seemed better. Then one morning I come out and again no reverse, so I took it to local shop. They said it had codes P0731, P0732, and P0733 and 1599. The latter they weren't too concerned about. They cleared the codes and the car ran fine for them without issue, they put about 100 miles on it and no problems. They tested the electrical and it was fine, they tested the pressure and it was fine, no leaks, etc everything to spec. They tested the battery and it was at 14.4 so they said that not thee issue. So they let it sit over night and again no reverse and they get the same codes. They think it is the Valve body needs to be replaced. Is that the fix, or could it be the PCM is losing the codes over night and then the engine is confused when we start it up and throws the codes? Anything else it could be with these symptoms? IT has a automatic transmission and fluid looks good. Just want to make sure this is the correct fix to go with. Thanks