Yes

yes

Tough call.

If the AI is smart..... Yes

If the battle AI was like in Medieval 2 Total War.... No

For me it would depend on the AI, will it be willing to take "safe" risks to get the advantage as a human would and know when the risk becomes too great? I'd hate to play a game where multiple competitors died in the early game due to pushing the limits.

Personally, I'd like an option for sovereign loss -> next in line gets the throne--particularly because it makes marrying off all your kids off for champions a bit riskier.

I can picture it now. You lose your sovereign in a battle, and the throne passes to the one with the strongest claim... some other faction.

Man, I've been playing too much Mass Effect 2- I was sure you asked if the game should over if Sovereign from Mass Effect 1 died..

Yes if no heirs are apparent.

Both. More options = more awesome

Though I imagine I'd choose 'yes' more often

Yes

The danger with the Yes vote, me included, is will players then wrap their sovereigns in cotton wool. Never exposing them to danger. This may lead to boring games, or games that quickly turn into King killing games. Strategy may go out the window!

Yes.

(After all, if you save you game prior to the battle, isn't that the same as 'no'?  Unless the game wouldn't let you reload saved games of that sovereign...hardcore).

I think that either way can be done well. For me, it depends on whether it makes sense with the story. 

Ah yes, good old D2 Hardcore, you die game over, and there is no reloading. I remember losing my cool more than once because of that.

Yes.

(Or Both, but that wouldn't affect my decision.)

Yes for no heirs.

No, just levy large penalties on military and economic factors to reflect the chaos created by the Soverign's defeat. While he "recovers" (think Sauron in LOTR), these penalties are in place. You can tweak the magnitude and duration of these effects to balance the game.