Computers should not be replaced as a guess. That just introduces a whole bunch of new variables to the problem. It sounds like the old one did exactly what it was supposed to do.
There are two speed sensors; an input sensor for crankshaft speed, and an output sensor for the axle shaft. The computer knows how fast the output sensor should be reading compared to the input speed based on programmed in values. When slippage is detected, the computer shuts the system down but keeps the diagnostic fault codes in memory.
The good news about this design is the computer constantly updates its shift points to give you a nice crisp, solid shift, compared to older transmissions that gradually developed sloppy or mushy shifts as normal wear occurred. The bad news is that you have no warning or clue that this wear is taking place until the day comes when the computer can't overcome the wear. When the slippage occurs, the computer shuts the system down. The shift solenoid pack is spring-loaded to allow you to use Park, Reverse, Neutral, and forward will stay in second gear so you can drive slowly to a repair shop.
If you suspect slippage, you can overcome it for a while by accelerating harder than normal, then letting off the gas just before the problem shift is about to occur. Slippage is much less likely to occur when there is less load on the clutches.
Your mechanic will connect a hand-held computer to read any stored diagnostic fault codes. If there are none, he can also read out the " clutch volume index" (CVI). These numbers will tell him the volume in c.C.S of fluid it takes to apply each clutch. This will give an indication of how much wear has taken place in the various clutch packs.