I actually just dealt with this for the first time tonight, and I'm fairly sure it had to do with a mixture of swallowing air and the strength of the liquid I was using. Nicotine seems to trigger a throat tickle for me, which normally doesn't do anything, but this time around I started hiccuping and coughing from it..cut the remaining liquid in my tank with VG and it stopped immediately. Might be worth a try if you're vaping high-nic or high-PG mixes, just add VG to taste, of course that'll dilute your nicotine level down, perhaps an appreciable amount depending on the strength you're using already. I hit 30-36mg liquids so cutting to 24mg doesn't make much of a difference, but if you're dropping from 12 to, say, 6 or 9mg nicotine from diluting it, you might have other issues like chain-vaping.
ETA: Also try the mouth/nose inhale method with vaping, it didn't work for me but a lot of people swear by it, basically you only inhale the vapor into your mouth and exhale through your nose. Supposedly you still absorb nicotine doing it that way, and it bypasses the lungs and throat almost entirely, which might help keep you from swallowing vapor/air and burping/hiccuping.