Hey, I've read in Men's Health magazine, and other health books, that all men have morning erections! Mostly while we are sleeping at night. That's if you're healthy with out any problems.
I think yours have just tapered off/stopped by the time you awake. I'm 48 and I still wake up with one. Not every morning, but most. Sometimes it only last a few minutes, sometimes just 30 seconds, long enough for me to get to the toilet, and then it's gone. I use to think it was just because I had to urinate, but I've learned that's not true, because there are those morning when you have to pee really bad, and theres know erection present. So, long story short, if you asked a doctor he would ease your mind by telling you that you're okay, and yes you still get morning erections, you just don't have any by the time you wake.