In the film franchise we see the Terminator(s) get shot, burned, flayed and smashed. In T1, it begins to rot without medical attention. In T2, Uncle Bob tells Sarah Connor that it will heal as she treats the multitude of gunshot wounds it has sustained. Does the skin regenerate, scar, or? At what point does the biological portion of the Terminators fail to heal?
In the original Terminator, Arnold was purposely sprayed with Vaseline to give him a look that he was constantly sweating. One theory was that the heat generated by the Terminator itself warmed the skin causing it to sweat. Eventually, this elevated temperature would kill off the tissue. I'm not a biology expert so I cannot attest to how long this would take, but it does make long term sustainability of the tissue difficult if not impossible.
Another theory was that the tissue placed directly on the endo-skeleton would react adversely to the metal, and attempt to reject it much the same way an artificial joint may be rejected by the body. This would cause the entire organ to react as though it were fighting a massive body wide infection. Again, this infection fever would make long term sustainability of the tissue very difficult to maintain.
To answer the question "At what point does the biological portion of the Terminator fail to heal", it's simply a balancing act between an infection, and whatever immune system is present. As soon as any infection tips the scale, the entire tissue system will eventually be lost. Because of the fact that the organic portion was in a stressful environment placed on top of the endo-skeleton, any infection would have a greater advantage from the onset.
The above information was taken from the following website: http://www.jamescamerononline.com/TheTerminatorFAQ.htm
This website is not offically a James Cameron website, but is billed as the biggest James Cameron fansite on the web as reported by http://whois.domaintools.com/jamescamerononline.com
In the first terminator we see the least amount of effort to perserve its skin. While it does do a little bit of work (removing the damaged eye) it is obvious his skin is not holding up to the strain of the pursuit. That terminator was always close to its objective though. It probably weighed the likelyhood of success in a given timeline over the importance of maintaining its outer cover. If the trail had gone cold the terminator might have taken the time to reestablish a passable outer layer.
In T1 the terminator is always close to its target, always on the verge of winning. In T2 they are going for evasion, crossing the border and disappearing into central or south America would have made finding very difficult. In T3 the terminator's objective to to secure Kathrine Brewster (and ultimately John Conner) in a secure facility to insure their survival of the immenent Judgement Day.
If you take the Sarah Conner Chronicles as canon; the artificial blood compound around the combat chasis provides very fast epidermal growth. Given proper treatment and baring some type of infection this should allow the terminator's skin to heal quickly.
We see this from Cromartie in the tv series. Upon reuniting its head with its body, it then proceeds to reconstruct an outer skin layer and to receive plastic surgury. It knows that without any leads it will need to begin at square one again.