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.
New Answer Derived From Exhausting Initial Answer & more:
It's your Water Heater, here are some things to try in determining whether or not there's actually a problem.
1 - Drain & clean the tank properly. ONLY do it when the pressure's good. Turn off the Hot & Cold Water & WH, open the T&P valve & drain the tank (see manual) to somewhere that contents can be seen. Blast on the cold water when you can start to "slightly" rock the tank to stir & break things up & periodically continue this until it's empty. Operate the hose bib handle to crush any big particles or Poke into your fully open hose bib if the hose flow drops. Then, when empty blast on the cold water & let drain & repeat until nothing comes out. Then, do just a 2-minute fill & drain & blast again to get all remnants out.
2- Check your status lights to your manual for detected problems.
3- Status Lights will also indicate a problem with the heater's Gas Control valve. But, this could also be a Gas Meter response to a run-away or leak detector, improbable since flow-rate wouldn't have changed.
4 - This is a pretty cutting edge unit you have & everything's interconnected. The fan & burner won't outrun each other & there may even be a Water Exit Regulator involved to turn the heater, sort of, into a Tankless Water Heater.
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Original / Initial Wrong Answer: If you have a Hot Water Recirculating Pump somewhere else, you're driving its thermostat batty & it's only now showing signs of needing attention. It would be stealing pressure until it's reading hot water again. You may have noticed the pressure returns after 10 to 30-minutes, when the Water Heater has recovered enough or recovered fully.
Best Answer
A nearly-full-clogged cold water pipe. Pressure builds in time after the clog (giving the initial full blast) but it cannot sustain the flow (dropping to a trickle).