Depending on which transmission you have, since there are a couple of possibilities. Ford used either an E4OD or a 4R70W. In both cases it seems that you're losing pressure on the forward clutch circuit.
With the 4R70W, you might have a defective 2-3 accumulator piston. Forward pressure applies against the back of accumulator. If the piston is torn or has excess wear it will not retain enough pressure to hold the clutches on. You may also have a sticking pressure regulator valve in the valve body. Either of these situations can be corrected without major work, providing that a pan inspection doesn't reveal excessive debris. Another thing that might cause this problem in the 4R70W, is worn sealing rings on the back of the pump stator. Generally these rings won't wear too much unless there's another problem. Too much endplay would cause this, but that would indicate something like a thrust washer or bearing has failed inside the unit.
In the case of the E4OD, there are a few things that could lead to your problem. One is a worn center support. If the support is worn where the forward drum sealing rings ride, it won't retain adequate pressure to apply the clutches. Another problem, though usually rare, is a sticking pressure regulator. Unfortunately, with the E4OD, you need to pull the unit. With that transmission, the regulator is in the pump, and not the valve body like the one in the 4R70W.
There may be a few other things that might be the culprit, but I think I've covered the most common areas.