Most of the vehicles that I bought had flaws, repair needs, this did not discourage me from the purchase. A tire pressure monitor malfunction is not a major problem, should not be a reason to panic. Would anyone advise a customer to avoid a purchase because of a TPMS malfunction?
To advise that “your vehicle is broken, see a mechanic” seems to abandon the repair discussion that the OP came here for.
Here in Maryland there is a required safety inspection for registering a newly purchased used car.* All the original safety equipment must be working properly. Sometime the beginning of the 21st Century I had a 1984 car fail that inspection because of a missing side reflector.** I’d guess that a malfunctioning TPMS would fail the inspection, too.
(* Inspection not req’d for transfer between certain close relatives. I can give my child a car with malfunctioning brakes, and it can be registered.)
(** I put on a replacement from a salvage yard. I kept several cars usable with parts from that yard. 
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In such an environment I would be looking for bargains on vehicles with easy repairs. A TPMS repair is not like replacing a crankshaft or transmission.
It’s all well and good for someone knowledgeable to buy a “fixer upper” but the OP doesn’t appear to have your skill set. Personally, I’d be put off by a “minor” problem based on experience with a couple of guitar amps and one particular Oldsmobile that just needed “minor repairs” because those repairs aren’t always minor. Instead, they’re symptoms. If “it ought to be easy to fix,” the seller would have fixed it already.
Further, the TPMS is either a bigger problem than you think, since the OP’s mechanic hasn’t been able to fix it, or he’s in over his head.
To advise, “Your vehicle is broken and your mechanic hasn’t been able to fix it so maybe try a different mechanic” doesn’t seem unreasonable. And recommending a mechanic for someone who can’t do the repair/diagnosis him/herself is also reasonable.