It's taken three years but it appears the problem has been resolved. Having involved Furuno USA and then Furuno Japan, we were advised a new software version - 2.13 - had been launched which appears to have cured the HEADING MISSING warnings.
Furuno has simply increased the delay before a warning is sounded from 1 sec to 5 secs. So the unknown reason for the intermittent heading missing warning has not been addressed, just the time delay before sounding the warning giving more time for the heading data to re-establish.
Is it a bodge? I think I have to say 'yes'. Do I care? No!