Well, one thing a Time Lord (or a Nyrond) might do in that situation is a sort of reverse I Say, James, changing sides several times and sabotaging both régimes. The trick then would be to make sure the sabotage was total on both sides, so that neither had the advantage.

As I said in a comment somewhere else, I don't actually believe in carrying on fighting when faced with certain defeat. At best, there's always another way; at worst, alive offers more options than dead. (Both old Nyrond proverbs.) The thing about learning stuff to use next cycle is that dead people, especially those on the losing side of a battle, are rotten at passing useful knowledge on; or in the words of an alleged old Scots proverb I found in a book yesterday, "A man's little use when his wife's a widow."