I tend to get extremely attached to characters in almost every game I play. Probably because I'm a hard core role player when I play, and I wouldn't delete myself, now would I? That being said, while it pains me a bit, if I am required to start a new save for new content then I do so. Otherwise, I play the same character always.
A good example of this is Fable 3. When I finished the game, I didn't necessarily start over and play again. I'd often load up the game and role play the good father/ruler. I can spend hours pampering my little virtual child. Ah~ Fable 3. Wasted potential, it could have been so much better. Not that it was awful, the spirit of a Fable game was technically there, but it was watered down. It didn't even have the chicken kicking game. Also, that rpg game quest is annoying after the first time. If it just had an actual good reward, it would be bearable. Personally, I think that you should have been able to choose whether you were saving a prince or a princess, and then at the end when kissing the cutout, it should have turned into a real live marriageable npc. Maybe a fairy prince/princess (minus wings)? Turns out the cutout was enchanted, the gamer dudes will also act surprised, like "what, now how did that happen?" The game's lacking unique npcs anyway, always looking for an excuse to add a few more. Also, their children should be unique, since they're royalty and so are you. Fix that bug where the children always grow into rags if you don't off your spouse before they grow up. Add more actual quests to when you're the ruler. Like, they missed the opportunity to have a quest where you choose a jester, and one of the options is a dude dressed like a chicken.
It would have been nice if children could actually use the gifts you give them. Wouldn't it be utterly adorable if your child used the toy sword to play fight, maybe have duels with other children, and could kill beetles with it?
I should also note that the child's bed thing is dumb. You can just have twin beds. More practical since adults can reasonably use them, too. Also, why did no one actually sleep in the beds? Fable 1 could do that. I feel like they rushed the game.