Hi I am having this same issue on my Cooper S (59 plate). I have only just bought it with a 2 month warranty from the (non-mini)dealer so I took it into Mini for a diagnosis and they tell me that the coolant thermostat is reading at 207 degrees C even when the engine is cold, so the car is trying to cool itself down constantly and therefore not accelerating as normal in case of over heating. There is also a leak at the water pump.
It needs a new thermostat and coolant housing and new water pump which Mini quoted as costing £500 for parts and labour. The dealer where I got the car is saying he can do it for £250 and therefore wants me to take it back there to be fixed, the only issue I have is that it is a 200 mile journey so it is going to cost me a lot in fuel and then I am worried that even with these parts fixed the flat spot/acceleration issue may not be resolved. I suppose then it will be up to the dealer to rectify the problem but it could end up costing me a lot in time off work and travel to keep going there.
Has anyone had this issue resolved in this way? I'd like to know if I would be better off just asking for a refund on the car while I still can.
It only has 36,000 miles on it so despite it's age it is in good condition other than this flat spot issue. The mini garage told me that the turbo is working perfectly and there were no other faults found on it when they did the diagnosis. They seem to think that fixing the thermostat/coolant housing and water pump will rectify it but they can't obviously guarantee that.
Any help at all would be muchly appreciated!