Power Steering on 03 Mini

[KCH1234]

My power steering goes after a lot of city driving (20 mins plus of stop and go) if I turn the car off and back on then magic it works again! I've had the system checked and there are no leaks or electrical issues with the car. It's a 2003 with 154,000 miles, I'm the second owner but the first was a family member so I know the car history.
Anyone have a similar problem and want to let me know what it could be and how much it may cost me?
Thanks!

[bad venge]

sounds like the fan is failing and that overheats the pump and it shuts down

[KCH1234]

Originally Posted by bad venge

sounds like the fan is failing and that overheats the pump and it shuts down

Thanks! And turning the car off/back on resets this? I know I need to bring it in to get it checked out but I'm afraid of what they'll tell me is wrong and how much it costs - plus I'd explained the problem to my regular mechanic before I moved and they didn't find anything