Hi Brad.
There are a number of problems that can cause symptoms similar to what you're seeing.
I'll lay a few assumptions, ask a few questions, and then cover what I've seen most often.
I assume you're in a medium size single family home (2-4 bathrooms, 1 kitchen, 1 laundry), no recirc. (failed check on a recirc. could cause this issue).
I assume you've had both the faucet and the Rinnai for a significantly longer than you've had this problem, and that they were working well when first installed. I assume this is not just an extended cold water sandwich.
I assume there were no recent plumbing work or repairs prior to the onset of this problem, that you are on city water, and do not have a water softener or a filtration system.
I assume you're a bit handy, and willing to do some testing yourself.
Is this always a problem, or does it appear and disappear?
Do you know the age of the house and the type of piping?
Can you give us a rough idea of the floor plan?
How many stories? Any under slab piping?
Is the kitchen faucet the farthest fixture? Any unusual fixtures?
You said you tested the kitchen faucet with the cold water supply turned off; did you get any water out of the faucet when you did a that?
The most common thing I've seen to cause temperature issues in a single faucet is some form of crossover, usually caused by a failed cartridge in a single handle faucet, a uncontrolled mixed shutoff(mop sink, shower head, etc), or a failed mixing/check valve. Essentially a lower pressure drop makes it easier for the system to pull water through the crossover than through the piping.
To test for this, turn off all isolation valves for other fixtures including laundry and turn on your kitchen sink. If tub or shower valve stops are not accessible, you can try turning the tub or shower valve on during the test(the pressure drop should prevent crossover), though that is a less precise test.
Second most common issue is some sort of heating system problem, though that usually doesnt show up as a single fixture problem. A typical Rinnai needs 0.5gpm to call for heat, and 0.25gpm to stay running. A lot of problems can happen with this system; flow rate is the only one I can think of that would only affect a single fixture. What is the flow like on the kitchen faucet? Can be a problem with high/ultra high efficiency fixtures, systems with hard water or lots of debris, galvanised piping, and water filters(though DHW rarely get filtered).
You can test for this by running hot water on another fixture and concurrently trying the kitchen faucet; if another fixture actively has hot water while the kitchen does not, the Rinnai itself is unlikely to be the problem.
Other problems becomes increasing less common, at least in my neck of the woods. I would check for them after testing for the obvious ones.
Good luck! Let us know how it turns out either way.
Thanks for the thorough reply! Let me see if I can shed some light to your questions:
I bought the house about a year and a half ago, and this issue seemed to arise slowly but surely after purchase, with no changes or renovations to the plumbing system or heater.
House is a single family home, 1 story, 4 bed 3 bath, 1 kitchen, 1 laundry room, built in 1979, all copper throughout, and per permit records, majorly renovated kitchen in the mid 2000's. On city water, and no softener system. Not sure exactly what a recirc is, but let's assume no. Likely not relevant, but I'm not sure where exactly the cold supply comes into the house (Under slab maybe?). I see the pipe from the main cut off valve over to the Rinnai, then just one pipe up into the attic from the Rinnai, obviously the hot side. (When I turn off the only valve at the hot water heater, cold still flows through house)
The kitchen is actually the closest faucet to the Rinnai. The laundry room is second closest, and the mud sink in that room (or at any fixture for that matter) will flow piping hot water at the same time the kitchen faucet is turned to hot, but water flows room temp at the kitchen faucet.
This is always a problem, you may get a hint of hot water for 10-15 seconds at times, but quickly fades to room temp.
When I tested the facet with the cold supply off, no water flowed when the handle was set to cold. When the handle was pointed up which is the hot side (single handle faucet), water flowed, just not hot.
The flow rate you mentioned really had me thinking that could be the culprit, but thinking about it, when the kitchen faucet is on hot, and I can go around the house to other fixtures and get hot water on-demand, we know it's not a pressure thing since other fixtures are pulling hot.
Hope this helps push us toward a possible culprit. Thanks a ton!