Thanks, Pool Clown. Yep, that fixed it. Basically, I initialized the IntelliTouch Outdoor Control Panel to factory default settings, after which the system is SUPPOSED to automatically load the previous parameters that remain on the Indoor Control Panel. Very slick design, makes it easy to reflash firmware or replace system boards without reprogramming everything from scratch.
Either I didn't perform the steps properly, or the system just didn't quite make it that easy. After the reset the Indoor Control Panel wouldn't respond, AND the Intelliflo pump wouldn't communicate with the system either. After thrashing about for awhile, I got the Indoor panel back to normal by performing the LOCK ON ADDRESS procedure suggested in the Troubleshooting section of the manual. Unfortunately the info is spread around throughout the manual, but I got it done.
The pump still didn't respond to commands, so I got that fixed by using the Indoor panel to specifiy it as an "Intelliflo 4" pump, and assigning it some Circuit Names and associated pump speeds. That was CRITICAL. Without the Circuit Names the system had no way to find the pump and communicate with it.
Now it works perfectly for extended periods, with NO PAUSES! Fantastic. I'm delighted.
Thanks to all for the suggestions that pointed me in the right direction.