No solution yet. I have tried reducing the amount of data loaded onto the unit, and that may have helped speed things up, to some degree, but it's hard to say without more testing. I just removed the domains from attribute fields for the related table, simplified point labels, and removed several ancillary data layers, so we'll see if that helps. Partway through editing a record in a related table, the dropdowns would just go blank, and ArcPad would freeze up. Right now, there are so many other bugs (e.g., query forms that don't work, glitchy hardware), that it's hard to even try to troubleshoot.
I was told that there are significant issues with ArcPad 10 & Windows Mobile, and that some of of these issues might be resolved with ArcPad 10.2 due to the adoption of SQL Lite. Apparently there is an Android version of ArcPad in development -- it really couldn't be any worse than ArcPad 10 on Windows Mobile, and it would provide more options for devices.
If the fixes I just tried don't resolve our problems, the next solution will be to go back to paper data forms & Garmin GPS units, which never seem to have the kinds of issues that ArcPad always seems to have.