The official service intervals on a MINI are no more than 2 years apart.
If your dealer services your car with more than 1,000 miles to the due date BMW will not pay them for the work, hence their reluctance to do it. However, if you get to 2 years old before the 10,000 miles they will get their money, as this is the maximum time allowed between visits.
It's a good idea to top your oil up, though, if you are going this length of time without it being changed.
As for never using up your TLC vouchers, if you hit 5 years old before having your 10k, 25k and 40k services done then tough!