Any chance that there's a problem with the radio itself? It'd be
one of those obnoxious intermittant problems then.


There is always a chance. Be sure to read the manual about SSB and Sync
mode.
I suspect the problem is Operator Error ;-)

Turn the mode switch to the Normal position while tuning.
Switch to Sync mode only when you wish to Lock in an AM station and listen
to the program.
Sync mode can not function when trying to hear a LSB or USB SSB signal such
as Ham or utility stations.
Sync mode requires an AM carrier to lock which SSB (LSB/USB) does not
provide.