Have you checked the fluid level? If the level is good it could be that the fluid in your transmission is breaking down once it warms up. A lot of MINI drivers actually like running Red Line transmission fluid. Have you ever replaced the fluid? We have a lot of great info about the fluid change for the 6 speed Agitronic transmission here:
Pelican Technical Article: MINI Cooper - Automatic Transmission Fluid Change
Red Line fluid for your transmission is D4 ATF here:
Pelican Parts.com - Red Line D4 Automatic Transmission Fluid and don't forget the filter here:
http://www.pelicanparts.com/catalog/SuperCat/6319/MIN_6319_TRAUTO_pg1.htm#item3
Try that out and see if it makes a difference. Let me know what you find out.