How do you prevent deliberately losing in Republic of Rome?
If it's not part of any sort of larger tournament or ranking system, then there's pretty much no difference between everyone losing and a draw, so it's just going to wind up being an issue of perception.

The solution, then, would be to play it in the context of a ranking system or tournament. I don't know the game in question, so I don't know what the possible outcomes are, but you could assign different point values to different results; winning gets you 1 point, losing gets you 0, and Rome falling gets everyone -1. Then people will have an incentive not to let Rome fall; if they do, they will lose rank compared to other players not in that game.

By the way, this sort of brinksmanship between the fall-of-Rome-is-a-loss and fall-of-Rome-is-a-draw crowds may be an intentional feature of the game. After all, it's not all that uncommon for some politicians or political parties to focus so hard on winning their own particular issues that they're willing to put the whole country at risk (state, nation, empire, what have you) if they don't get their way. It sounds like a pretty realistic political situation, if you ask me.