Thinking about how I would be playing the game: if Sovereign loss cost is too high, I would simply save before each combat, and load if the result is not to my liking. That would negate the whole point of imposing penalties for losing the fight. So, speaking for myself (and, I suspect, a great many gamers who are not nearly as hardcore as most of the people here), imo either the cost has to be 'just' but low enough that most gamers will simply take it and get on with the game, or there should be an opt-out in the game creation screens for something like the aforementioned.
----
I don't know where the overall flavour of the game is heading, but if I might suggest something, partly my own, partly borrowed from others who have already posted:
1. In own territory, whether attacking or defending, the sovereign counts as defending his own lands, and will always escape when losing "Local inhabitants helped the Sovereign to escape to the nearest city." Then put the sovereign in a city nearby that does not have enemies right next door (if available), put him out of action for a turn or two to heal. (And if he's then attacked in that city and loses again, it's game over?)
2. In neutral or allied territory, "The Sovereign escaped the disaster, and after much hardship, returned home." Sovereign is relocated all the way back to the capital, and is out of action 5 turns or so, recovering from the ordeal. (This would allow the sovereign to be used for initial exploration.)
3. In enemy territory, a loss, in attack or defence, can result in the Sovereign being captured. (The sovereign should always be the last unit in a stack to defend, except if the player changes that). If he escapes, see option 2, if not, the war ends, and depending on relative strength, the enemy takes techs, money, and/or cities. If you've got nothing of value to trade, i.e. you've all but lost already anyway... (Maybe an option for the more hardcore, if you deny the ransom demand, the sovereign is killed, and a successor takes the throne (i.e. you receive a new sovereign at either base, or at least, much lower level.))