Why does my kitchen faucet stop and start at full pressure only for a split second, both cold and hot?
This symptom is common with external sprayers. The diverter causes water to shutoff from the faucet when the sprayer is in use. The external sprayer may be leaking (into the sink, or under it) or the diverter valve itself may be failing. If you have a sprayer, check both ends of the hose for leaks and fix that if you find any. If not, remove the valve and make sure there's nothing that can be easily cleaned or a bad washer that can be replaced. As a last resort, take the valve to the store to find an exact replacement.