I don't think it's really a matter of how much someone cares, its just that people get comfortable/used to what they have around them. For example, if you're in a long term relationship, it doesn't work out, and you guys break up, you have good reasons to break up, but a few weeks/months later, you regret it because you miss having someone around, the memories, etc. During this time is when you realize all the good things and push the negatives aside, and to me that's when people realize what they've lost.
This isn't for all people, of course there are the ones who recognize all the good stuff DURING the realationship, but I'm sure everyone will come across a situation like this. Appreciate as much as you can, and if it dosen't work out, then you can't say you didn't appreciate.