Transmission disengages from gear when car gets warmer it gets worse

When I start the car and select drive, 25% of the time the transmission gears(?) Will engage, and move the car forward (jerky). The other times it behaves as if it were in neutral, and I can rev sky-high with minimum/no forward propulsion. If I select reverse, it'll catch on 50% of the time.

If the transmission does go into gear(?), I'll cover about one mile of roads before on some innocent upshift the transmission will behave like being in neutral again and I'll lose momentum (no acceleration) no matter how much I step on the gas pedal and rev high. Talk about embarrassing in the middle of a busy intersection. I have to pull over, shut the car down, and restart the car and the transmission will upshift normally briefly for a small distance. And then it happens(behaves like neutral, possibly popping out of gear?) Again, and again, with the only temporary remedy being shutting the car down and then restart. Once I had to shut the car off five times to cover one mile.

Transmission fluid levels are fine.