The valves inside the valve body on the underside of the AOD are stuck. This is probably the 1-2 valve. As the car is driven, the fluid heats up and the bore where the valve sits expands and it frees up. I experienced the same thing when I accidentally had an extra spring on my 2-3 shift valve. It would go to the point where it was supposed to have shifted ...around 2000 and it stayed in the gear. I took my foot off and it neutralled until it returned to the lower speed where the shift point would have been and then it kicked in.
First...check the fluid level. A low fluid level will make the car slip out of gear until you throttle it up some and the forward pump sucks whatever is left in the pan into the transmission and it takes off suddenly. If that looks good, drop the transmission pan, observe where everything is and then drop the valvebody. Take it inside and CAREFULLY take out the 2 bolts holding down the backplate. There are springs and such in there so a photograph would help in case everything gets knocked over later. Now comes the fun part.
Probe the connections. Most are held in by clips or sliding plates. Push the sliding bores from the top with a screwdriver or just take each apart in turn and see how well each of the drums slide inside the bore. They should all move freely. If they dont, you have your culprit. Take it out of the bore and roll it in some steel wool or 600 grit for a few turns and reinsert. Keep doing this until it moves freely and keep going until all valves move freely, reinstall, refill and go for a drive! Make sure you torque the valve body bolts to only 24(?) ft lbs or so. Overtightening them will pinch the valve bores together and you will be right back where you started.
Or just get a lentech valvebody for a huge performance increase to boot.
Good luck bro!
CrazyPete