So, I was out in the middle of nowhere fighting some bandits, and Vigilance randomly ran away when the fight ended. Entering a new area didn't bring him back. Is there any way of getting him back?

He probably got killed. Took me a while to realize he was gone so I went spelunking in the caves I just cleared to look for him. Yep. Dead as a doornail. Gave me a decent meal though... I was very hungry at the time. Maybe you wont have to eat your dog.

Okay so the first half of that statement might apply to you... Dunno.

No, he didn't die because he didn't run off until after we killed everything. Is there any way to get him back?

Not a clue. Maybe use the console commands to get him back? Other than that I'd chalk it up to one of those glitches that I roll play in my head as my dog ran away.