1-Series - run-flat tyres

I went for a test drive in a 1-Series today and was quite pleasantly
surprised. Once behind the wheel I forgot about its strange appearance and
started to appreciate its excellent driving qualities.

Anyway, the question I have is about the run-flat tyres. I understand that
if you get a puncture you can drive for a certain number of miles on a flat
tyre. But afterwards, can the tyre then be repaired or must they always be
replaced?

Having had 3 punctures in the last 10 months makes me a bit wary.

--
Richard