I don't know if I am just unlucky, but it seems to me that if you kill a dragon with the flames spell (could be others as well, I have only used flames at the moment) the dragon will not disintegrate and give a soul. This happened to me with the first 2 dragons you encounter in the main story line, so far. I have had to resort to console commands to complete these missions, as I defeated the first dragon 5 times and every time I never got the dragon to disintegrate after it was killed. It is really getting to me, I have always wanted to play as a destruction mage, but I can't even complete the main story with mine. I would appreciate a fix for this if anybody has one, I currently have the Unofficial Skyrim Patch v2.0.3

It might not be destruction spells,it could just be for some reason you can't absorb dragon souls.Try killing one normally and then see what happens.

I've only had that problem at a couple of dragon shrines, where I've already killed the dragon once. The second time I'm there & kill a dragon, it doesn't have a soul.

I think that your game is glitched. Something loaded wrong, & it keeps saving that way. In that situation, I would just start a new game.

I'd be inclined to believe that, if my ranger character also had the same issue. But it only happens when I kill a dragon with magic. I'm in the process of looking for another one now, I'll let you know what happens when I find it.