Is the TK-4 set up to also heat domestic hot water for the house? (An "open" system.)
If yes, is the Taco-0011 the either the bronze-flanged (-BF4 rather than -F4) or cast-iron body w/bronze cartridge (...-J) version? If not, it's possible the impeller is toast from oxidation, but that may not be the only issue with the setup.
Why such a monster-sized pump for a 1-room heating system? (You only need ~1gpm to get the TK-4 to light off, and unless this is an 8-car garage your flows to the manifolds don't even need to be that high.) I'll bet it's driving near the max gpm rating of the heater, which WILL wear out it's flow sensor (guaranteed!) Even the ubiquitous -007 is probably overkill here.
How are you setting the output temp- do you have one of front-panel remote controls, or is it a dip switch setting? (If you don't have the remote- buy one- it'll help figure out what's really going on here.)
Is the tubing suspended below a wooden subfloor, stapled to a subfloor, have heat transfer plates or... ??
How any feet (and what diameter) tubing do you have under the floor? How many loops on the manifolds (or is it one long snake?)
At 120F output with heat transfer plates and some reasonable flow you should be able to feel it. If you're over-pumping it with a very low delta-T between the output and return flow the internal controls may interpret that as a fault condition and not refire for some fixed amount of time, or until it has cooled to some temperature. If it's constantly going from 120F to 85F the average temp is barely over 100F, which means you won't feel much at the floor.
For the system to be able to run continuously you need enough tubing and heat-transfer plate to deliver 10,000BTU/hr into the floor (the minimum-fire output of the TK-4), with a sufficient drop in temperature from the output manifold to the return that the TK-4 doesn't interpret it as a fault condition. Water heaters have a maximum incoming water temp at which the controls will often interpret as a malfunction or assume to be a danger condition. With the TK-2 that temp was about 130F, no matter how the heater was being used. I'm not sure about the TK-4- it may be an absolute number, or minimum delta below the output temperature, or maybe it's ignored altogether. If there is a ball valve with which you can reduce the flow to achieve a bigger temperature difference see if that helps. With a remote control you'll be able to read both the incoming temperature and the approximate flow rate directly. Shoot for something under 4gpm, but over 1gpm (it still need enough flow to get the ignition to fire reliably). The lower the flow, the bigger the delta-T. At 2gpm with a ~10F delta (110F return) the thing should be able to just run forever, provided you have enough radiant floor to shed that much heat into the room.
But if you don't have enough radiant floor to dump 10KBTU/hr of heat into the room at the temp your running, it will still cycle on you. As the floor temp rises, so will the return water temp, and eventually the delta-T collapses to zero- the return water temp keeps rising. If you bump up the temp to 130F the floor can dump more heat into the room, but whether that's going to get you there depends on the total amount of square footage, etc.
If this is an open system, with insufficient radiation it's probably better to set it up with a heat exchanger and a small buffer tank, and a couple more (right sized) pumps. But it's still a real hydronic design, that requires at least the back of napkin math to get sorta-right.