It's easier to debug if you hook up the compatible remote so you can read the actual error code.
On units this old flame-sensor varnish/crud is always suspect. Cleaning it up with a plastic scouring pad like a Scotch Brite (and NOT SANDPAPER) will often do the trick. Turn off the power and the gas to the unit before pulling it apart, but it's not a big project. Once you've done it once it's even quicker/easier to do again, if need be. (Air contamination issues make this an annual ritual for some installations, but if yours made it 9 years without a problem it's likely that you'd go years between cleanings.)
Flow detector wear could be an issue too if it's only happening with lower flow faucets. IIRC the T-K2 needs to detect a bit over 1gpm to light up, and will flame out if flow drops below ~0.8gpm.