HI & Welcome to MINI2
Ive heard of faults with just one of the locks failing - my 2004 MCS
had a hatch lock failure - quite common on earlier cars & replaced under warranty...
...but to have everything fail - seems a bit more than bad luck or coincidence
So maybe its not the locks themselves, but possibly something wrong with the voltage / signal going to them is too low / corrupt - or maybe a close signal is being immediately followed by an open signal!
Or heres another (more likely) possibility:-
When any of the doors remain open - the rest will not (remotely) lock until the open one is shut ...
... so maybe one of the doors / filler cap is not triggering its micro switch that tell the computer that its closed - & therefore nothing will lock
Sounds like somewhere to start looking anyway - let us know how you get on