I’d presumed simply that he’d sustained enough damage to his flesh that gangrene was setting in. If you listen carefully you hear the buzzing of flies attracted to the smell. Evidently preserving the viability of the flesh shell was a low-to-nonexistent priority in that instance.
Hear flies? Heck, you could see them. they made a point of them being visible.
Preserving the viability of the flesh was important, because the Terminator had to “pass” as a person. A gleaming metallic endoskeleton with a rictus grinning skull face is going to attract attention and have a hard time interacting nonchalantly with people. The problem was that his skin had started to rot, and there wasn’t anything he could d about it. He was cutting away the damaged eyeball in order to allow an unfettered view of the world from that eye, but he was still careful to cover it up with his Gargoyle dark glasses.