From what I've read, ships only tended to be damaged to the point of sinking with regularity if:
1. The battle was a real knock-down, drag-out affair like Trafalgar or the Sinope.
2. Bad weather was involved (the unfortunate fate of the Spanish Armada)
3. The battle was a blockade (see a thousand famous break out actions.)
Sometimes ships would flee and sink after a battle, but I'd hope to avoid Empire: Total War scenarios where two fleets come in and 1/3 of one sails out.
That said, if the game does go into the 1820's we would be seeing early (effective) explosive shells, see Paixhan's gun. The later era ships would be much more capable of inflicting significant damage to each other and causing "insta-kills."
One thing I would suggest is that a captain who surrenders can, under some conditions, "volunteer" to join the enemy. Up until the Napoleonic era this was a very common thing. The Russian navy, the one I'm most familiar with, lived off of its foreign captains, which included a number of Scotts and one rather famous American. The same thing applied to officers on the ground as well, of course. Many officers would merrily join up with their captors under the right circustances.
Of course, the number of times a captain has changed sides would be known to his attackers (in the game) and thus they would be able to judge his trustworthiness based on that information.
Assuming nations are implimented in some fashion which gives them a presence in game, then it could be arranged for them to ransom captains.
Finally, if your ship is captured or destroyed and the enemy decides not to take your captain with them, it can be assumed that he finds a lifeboat and just happens upon rescue, or finds a desert island or somesuch.
Or, as an alternative, every time your character 'dies' you assume the role of his son/brother/heir, who recieves a letter (and possibly a coffin) informing them that they are the proud owner of whatever was stuffed in your warehouse.