I have a 2005 mini one, 107000 miles which has just experienced psp failure 2 days after I purchased from private seller. He may or may not have sold it knowing the fault was there... For me when it happens the steering goes so stiff without warning, but turning engine off and back on resets it and you can drive as normal for quite a while before it might go again.
After reading a post on this forum I took it to local mini dealer and explained the problem and requested help getting a goodwill payment.
Catch was the fault needed to occur during diagnosis (30 minutes) and if it didn't they would give me car back saying nothing was wrong. I decided to take it away for an hour in attempt to coaxe the fault out so I could get someone to diagnose it immediately. I managed it by leaving it idling for 15 minutes and driving around for half hour. I wrestled it back to dealers, left engine on and got the chap to come out and verify the fault which he did.
They were really good guys but explained they don't make the decisions when it comes to goodwill payment. With high mileage and buying private they suggested it might count against me... Good news was it didn't. They phoned me today and told me mini have offered 100% parts and labour. Only need to pay Ł60 something for the diagnosis/health check. Wasn't expecting 100% so have to say I'm really pleased with the service I've had. If yours goes I'd suggest take it to the dealer rather than try and fix it yourself.