Tom, I suspect that there might be a cabling issue that is causing the
radio to erroneously register a push of the "down" button on the
microphone (if that model is so equipped). I ran into a similar issue
with an FT-2800M a few years ago; that model in particular was also
susceptible to erratic behavior from RF coming in through the microphone
line.
I guess the best place to start would be to disconnect your APRS interface
and see if the problem persists. If it goes away with the interface
disconnected, it could be a cabling issue.
Steve
KG4PEQ