What was the original problem was it over heating or another fault ? Where in the world are you ?
If they think it's the head gasket why are they not doing a hydrocarbon check quick and simple job takes 5 to 10 min to do it.
If it's loosing it fast and they think it's the head gasket pull the spark plugs and look in the cylinders with a borascope
It's hard to say with out seeing the car but if the cooling system is not bleed correctly or they have used the wrong spec coolant it is possible to have this problem you describe.
The system must be bled properly there are a lot of posts here about it.
The coolant tank on your mini is not pressurised like the cooper s it's only a tank and to initially fill the system everything must be done with the rad cap off And bleed correctly.
Hope this helps will try find you a link for the cooling system bleeding http://www.mini2.com/forum/maintenan...screw-plz.html