The collagen that holds together scar tissue is continuously degraded and replaced. (Plastic and Reconstructive Surgery, 1976) If collagen synthesis slows down, due to scurvy for example, old wounds can in theory reopen. Historic records of sea voyages contain descriptions of long-healed wounds opening back up in scurvy victims, and these cases are cited authoritatively in some papers (e.g. Annals NYAS 1961), but it is difficult to test experimentally.
I would describe this more as 'maintenance' of the scar, rather than as 'continuous healing', but it may be of interest to you.