When we first got Pinkie, we didn't leave her alone for one minute until she was almost a year old. If we weren't home, she went everywhere with us. She's never suffered from separation anxiety, although she'll pout sometimes.
Conversely, the male rescued dog I've had for almost a year has bad separation anxiety. When we first got him, he apparently would lie at the door from the time I left until I got back, but he's gotten better about that. I still can't leave him in their playyard with Pinkie and go back in the house, tho; he'll sit at the gate and whine & bark. He's glued to me everywhere I go in the house and even if he's sleeping, I can't go 10 feet into my bathroom without him following me. He's probably about 2 now, and it's something I work with him on quite a bit. He's slowly doing better, but I wonder if he's really ever going to get over it. He *was* abandoned and passed around quite a bit before I got him.
I feel that separation anxiety comes from insecurity and I try to figure out if it's something I'm doing, so I can correct it. I saw a documentary on human babies one time that showed how a mother playing "peek a boo" with her baby actually taught the baby that the mother was coming back after "leaving" and made the baby more secure.
I've tried that with Willie a couple of times, using bed sheets or towels, and his reaction is quite interesting. He's surprised at the new game at first, then starts getting quite agitated as I keep doing it - excited & playful, but also scared & not quite sure it's a game. I don't let that get too far before I stop the game and give him some loving & reassurance. He's getting better with it, so I hope it'll do him some good in the long run.
Now Pinkie? She knows it's a game and divebombs me from the other side. LOL
