There are a couple of areas that the leak is coming from. The pump seal is the most obvious, but it can also be leaking from the pump mounting "O" RING and the pump gasket. It is also possible that the reason for the leaking, the converter hub (or neck)is damaged and has torn the seal.
When you pull the transmission, check the hub. It must have a mirror like finish. If the hub is worn, then check the pump bushing, as that is normally the cause of excessive hub wear.
So called leak fixer uppers(seal swellers) are as others have said a waste of $$$$$.
If you're looking for a quick fix, put a tablespoon of brake fluid in the transmission and it will do the same thing.
The reason it quits running after you shut it off, the pump is no longer running and creating pressure.