P1125 and 1126 codes
 

P1125 and P1126 OBD code on 2003 Mini. Rough idle and dying. With the following codes P1125 and P1126 “Throttle potentiometer 1 and 2 measuring range or power output problem” (minor fault) and the 1126 (major fault). I changed the throttle module and reset the code using the iCarsoft scan tool. Had to reset a couple of times. The car ran fine after that. 4 weeks later EML light came on. Pulled over and got the P1125 code again. Reset with the scan tool drove another 40 miles with no problems. Starting car after 8 hours park time and the code came back. Reset drove home and parked. Next morning car will hardly run and dies at idle with code P1125 and unable to reset.

Hello there - first, is your '03 MINI a Cooper or a Cooper S?

P1226 Throttle - malfunction (flap malfunction)
P1125 Throttle - valve potentiometers 1 and 2 - measuring-range or power-output problem

When you got the EML light you only were throwing P1125? P1126 is not present at this time?

I have seen these items below replaced before for these 2 codes/issues:
13-54-7-509-043 Throttle Housing AS
12-51-7-520-939 Wiring Harness

Since you already replaced the throttle housing, it may or may not be related to the harness. You'll want to dive into that problem area a little more and see if it is possible that it's your cause.