I have a Saturn SL2, 2000, 110k miles, automatic. When the engine is cold, reverse works. After the engine warms up, reverse stops working. It doesn’t start moving from being in that gear, nor does it work when I push on the gas. Shifting from First to Second is a little rough at times.
Have you considered getting the fluid changed. If your Saturn came with Dexron III, upgrade to Dexron VI.
When was the last time it was serviced?? What you are describing sounds like the 2nd clutch is leaking when the fluid warms up. This is an issue which needs to be addressed by removal and disassembly of the transmission.