most likely the torque converter clutch is coming apart and this for whatever reason dumps a bunch of really fine "sediment" into the fluid which gets sucked up into the filter media and once it runs for a while, clogs the filter and you lose line pressure. Once it shuts off, the sediment settles into the pan and the trans will work briefly, until the sediment gets sucked back up into the filter. You may get lucky with just changing the filter and fluid, but probably need at least a torque converter to really fix the problem. Put the pressure control and TCC control solenoids in while you are at it. This happened to my tranny and many others. Dave at TEP can probably elaborate or vouch for this condition.
