It's a little more than a game, it's a pet! I don't usually feel sad when my Connection leaves, but sometimes it's a bit saddening when my P1 leaves. You know, P1s live ALOT longer than Connections, so it's easier to get attatched to it.
I had a P1 who I named Trooper once. He was a Ginjirotchi. It was a little sad when he left. I still miss him. So much, that a made a whole page dedicated to him on my website.
your tama will allways leave two days after giving birth, maybe show that you miss him/her by makeing a memorial on the tamagotchi memorial tamagotchi memorial
and you can still see her if you go to the parent list on your tamagotchi and go to tama town and click on the parents house and put the password in from the parents list.