Why does my kitchen faucet cut out intermittently?
I may be way off base here but have you tried removing the aerator on the faucet and letting it run on both hot and cold fully open (separately)? It's possible that the aerator could be clogging up and causing pressure buildup.

If you do not have copper pipes then it's possible that the buildup would be caused by rusting or oxidization in the pipes. Full pressure should knock it loose I think.