I have a 2007 Mini coupe with a manual transmission. Just recently it won't shift into the 6th gear.

 

Any trouble getting in to our out of any other gears? On the face of it, this sounds like the beginnings of TO bearing failure.

 

The first five gears work fine. It's almost like something is in the way to put it into 6th. There was no grinding at all.

 

Usually good to start from the top and work down. Maybe remove the shifter boot and check for some small object adrift blocking the way. Here's a step by step. Next step would be linkage.
http://www.redlinegoods.com/MINI07install.php

 

Is your car a 1st or 2nd gen car? This is a 1st gen forum.

Being a 2007 Coupe I would say that you need to do the following:

You may need to remove some intake components to get to the shift weight on the trans, clean the connections up and grease everything in the shift linkage on the trans.

We've had multiple cars that we have had to do the same with.