I'm kind of like you, I stopped playing Heimerdinger recently (very recently, within the past two weeks) since I've just been having a lot of trouble winning games with him. He's a champion that excels when he can stay in range of his turrets, but is very weak outside of that. I think the major problem, in addition to the lack of mobility that others have been citing, is that the enemy basically knows where you're going to be. Since you're strongest in the middle of your turrets, that's typically where you're going to stay, so it becomes easier to aim skills since there's a zone that Heimerdinger is more likely to frequent. Not to mention, taking out turrets starts to cut into his safe zone; champions with long range and that can do this really hurt Heimerdinger, since he doesn't have much long range threat (his missiles don't do huge amounts of damage until late game). If you can survive being insta-gibbed, you're actually very strong vs melee assassins, especially if they're silly enough to dive onto you in the middle of your turrets, but most people know not to do this (and most melee assassins will give up their outer turret to roam to other lanes, which you can't really counter since lack of mobility and lack of strength without your turrets set up).
Basically, Mages can take out Heimerdinger's turrets and overall out damage him unless he's in the middle of his turrets, which most mages can take out from afar. Assassins can get destroyed if they're silly and dive on you in the middle of your turrets (esp. if they have no escape), but if they're smart they'll just hold lane or just go roam and kill your other lanes, which you can't really follow up on since you don't have turrets set up. All this, plus picks like Ziggs and Xerath basically do what Heimerdinger does (hold and push lanes), arguably better than Heimerdinger, and also have global pressure and more burst damage/long range poke.