So, is the Takagi flame turing off when that happens?
If yes, does it fire up instantly when you open a hot-only tap, or is there some time-out period?
Do you have a remote control wired to it?
If yes, is it reporting an error code?
Scale-up isn't a the most likely culprit here, but you should de-scale it anyway. If it's scaling up enough to restrict flow, it could indeed be contributing to the problem. Scale buildup often results in lower heat-transfer efficiency- a more common symptom is the thing fires up, but not enough to provide enough heat at the higher flows even with flame at high. But in warm-water areas this might not be noticable until it's nearly blocked(?).
The TK1 doesn't regulate well at very low flow, and may be turning itself off if the hot-water side flow at the mixing valve is too slow. The fact that monkeying with the valves seems to "cure" the problem makes me believe this is in fact what is happening- when the HW flow gets high enough to re-fire you're back in business until the flow gets low enough that the flow sensor thinks it's stopped, or it can't keep the temp within-bounds at that flow and turns itself off.
The solution may be turn down the temp on the Takagi a notch so that you're running the mixers at the tubs it's a consistently higher hot-side flow. It takes 0.75 gallons per minute to start it up, and needs 0.6gpm to STAY lit. On the TK1 you need the remote to be able to raise or lower the 120F pre-set, but it's worth installing anyway since it can report self-diagnostics. (Search the internet & auction sites for the TK-RE01- it costs less than a single service call.) If you don't already have it, download THE MANUAL.
Yours is old enough to run into flame-detector issues (usually fixed by cleaning with a fine plastic scouring pad- nothing too abrasive) but that's not likely to be the problem here, since IIRC it won't refire without cycling the power to the unit if the controls have that error.