TPMS fault - Audi A1

[Valm]

The TPMS warning lights on my Audi A1 (2017 1.4 TFSI Sport) are permanently on display and I can't reset the tyre pressures on the MMI control panel (it's greyed out). The car has done less than 35,000 miles. 

My local Audi garage has done every type of diagnostic test and update, without solving the problem (it was in for over a week and I had a bill of ca. £1,000 for nothing...)  I was told they'd find another car with the same spec and swap over some parts to try to find the fault but they've failed to do that for the last seven months.

My MOT is due soon and all the garage can suggest is running the tests again with no guarantees of success (presumably with a similar bill). I'll need the cambelt changing soon but if it's not going to pass the MOT there's no point throwing more money at a heap of junk.

Has anyone else had this problem - any ideas on what it might be? 

Someone who had a similar electrical problem suggested it might be corroded alloy wheels. Prior to the TPMS warning light issue I had had frequent warning lights about various bulbs needing replacing. 

[Magnet]

Hello Valerie,

The answer may(in caps) be within your last paragraph. Corroded valve seats are not uncommon, and various warning lights appearing can be a classic symptom of a failing battery. How old is your battery, and have you had it’s efficiency checked? 
Since you are having TPMS warnings, what are your actual tyre pressures as measured on garage or tyre retailer’s air pumps? 
Kind regards,

Gareth.