My guess is that VCC is dropping far enough to stop the oscillator.  If VCC
slowly increases back to a normal level, the crystal or resonator oscillator may
not restart. (RC circuits are supposed to be guaranteed to restart.)  The
crystal or resonator schemes need a sharp VCC rise to kick start them.  The
circuit is really just an amplifier with a frequency selective feedback loop.
The sharp VCC rise generates an initial output transient that get filtered and
fed back for regenerative feedback. Without the frequency rich initial impulse
to drive the filter, there is no signal to filter.

If the oscillator does not restart, no code is being executed and the watchdog
does you no good.    An external reset circuit will not save you here, because
reset only restarts the code.  The oscillator circuit is independent of reset.
The ultimate fix, is to cycle VCC along with reset as has already been
described.