Indeed. You end up so attached to them, that when things start going wrong with RPG itself (like, problems with the group, etc), you feel like getting apart of a real someone who you like a lot... ^^'
And don't blame yourself as a GM. It might be only that your style of mastering doesn't promote much of leveling up. Which doesn't mean it's bad, at all. Maybe you promote more role playing (and less monster killing, thus less XP), what is a great thing - and, well, a slower game guarantees fun for a longer period, after all!
See ya! ^^