As far as I am concerned the question of whether AJ's parent are or are not still alive has pretty strong evidence on both sides.
On the one hand, AJ's parents being dead would explain some thing, like why Granny is raising them so young as well as giving a really good explanation of why AJ is so attache to that hat (remember that bit at the wedding where she did her "shifty eyes" to check if anyone was looking, and then put it on on top of her maid of honor coustume?) My theory used to be that AJ's parents gave her the hat, but now I am pretty conviced the hat might originally BE her dad's (Stetsons are unisex, and orange/tan is a fairly gender neutral color, so it could be a man's hat).
On the they are alive side, there is the question of Applebloom. But there is a bigger matter. Consider all of the OTHER ponies at Sweet Apple Acres (Apple Fritter, Red Delcious, Golden Delcious etc.)SAA is literally FILLED with ponies, and while quite a few look a bit older than AJ, NONE of them look old enough to be parents. The only two fully adult ponies Ive seen are Granny Smith and Apple Strudel. So where are all THIER parents? Appleoosa? I'm beginning to think there may have been a real tragedy in SAA's past, one big enough to wipe out a whole generation.