Prevent pipes from freezing

1) Guesses: Sounds like a bad single-handled faucet cartridge, or low water flow at faucet, or clogged water filter.
Replace faucet cartridge, clean the aerator, and/or clean sediment out of pipes below sink, and clean water filter at tankless unit each month.

2) For exact measure of problem:
Typical faucet can have 2 gallon per minute flow rate.
2 gpm flow rate means faucet fills 1 gallon container in 30 seconds. Test faucet using 1 gallon container and a cooking timer to get flow rate.
Clean aerator to improve flow rate. Compare kitchen flow rate with other faucets in home.
http://waterheatertimer.org/Low-hot-water-pressure.html

Most homes have 1/2" diameter pipe running to kitchen faucet.
100 feet of 1/2" diameter pipe holds 1.2 gallons of water. This assumes no sediment build-up inside pipes.
http://waterheatertimer.org/Water-heater-recirculation-system.html

Assuming only hot is turned on: If faucet is 100 feet away from water heater, and pipe diameter is unobstructed 1/2" diameter, and faucet has 2 gallon per minute water flow, then hot water should arrive in 36 seconds.
50 feet away, and hot water should arrive in 18 seconds.

If kitchen has single handled faucet, and the handle is raised in the middle, then equal amounts of hot and cold water are drawn at same time. This doubles amount of time for hot water to arrive.

If single handle faucet has a bad cartridge, then faucet can have crossover.
Crossover means that cold water can enter the faucet even if faucet is turned to hot.
Bad single-handled faucet cartridge can delay or stop the arrival of hot water.
http://waterheatertimer.org/Crossover.html

Tankless require maintenance including cleaning combustion parts yearly, de-lime heat exchanger frequently, and clean water filter each month.
http://waterheatertimer.org/pdf/Tankless-maintenance.pdf
http://waterheatertimer.org/pdf/Bosch_Overcoming_fluctuating_temps.pdf
http://waterheatertimer.org/Troubleshoot-Rheem-Tankless-water-heater.html

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If your posi-temp valve is working correctly this should not be a problem. Does your hot water temp. ever get extremly hot or just warmer? The way the posi-temp cartridge is designed if you have a large drop jn cold water pressure then the inside piston is supposed to slide to the hot side restricting the flow of hot water to a safe level.If the pressure on the hot side drops suddenly then the valve is supposed to restrict cold water flow.
If the temperature gets to a unsafe level you can adjust maximum hot setting by removing the handle. There is a allen head set screw on the bottom of the handle. Loosen screw and pull handle off. On the newer models pull off chrome sleeve from around valve body and slide outer geared disc off enough to seperate from inner gear. There are markings on disc with arrow pointing to h. or c. Adjust outer disc in the direction you want to adjust and slide it back so that gears engage. Each tooth on gears will change water temp. about2-3 degrees.Try it and readjust till you get the hot set point you want. One other thing you could do is install a small pressure tank on cold water line to compensate for pressure changes. Hope yhis helps you. Thanks

Hot water line connected to left side of faucet? Did you replace tap set, or just cartridge? Cartridge may be out 180 degrees.

start by making sure the valve that supplies hot water to the sink and dish washer is fully open. If there is low hot water pressure in any of the other kitchen/bathrooms, then trace the line to see where the pressure drops. If it is only in the kitchen, it should be an old valve, (causes restriction)Good Luck.

did you replace the faucet cartridge??
if you did, you need to take it out and turn it 180 degree (not head to toe). the water control is on reverse.