I'm gonna go ahead and ask a stupid question: are you in the right gear? I once rode with a guy who was very strong on the straights, and even up inclines, but for some odd reason, he was shifting to a harder gear when coming to a stop. I think his thought process was that he could put more power down from a stop, but what ended up happening was me leaving him in the dust after every stop.
For my bikes, I generally know what my best "start" gear is, and make sure to be in that gear every time I come to a stop. An easier gear helps you spin it up more quickly, and therefore accelerate faster.
But if you're doing all that, then yeah, interval training is probably the only way. Or just blame it on the bike and get a new one. That always works.