I have tried 3 times to grow this alpine, aka 'Fairy Thimbles' in a
container without much success.

I bought and planted it out again in May into a container which has
other alpines. It flowers well during July then completely dies back by
the end of August and usually doesn't regrow. This year it has died back
again, but seems to have produced a new set of leaves about a couple of
inches away from the main dead crown, and so far they seem OK, but it's
early days.

My other alpines in the same container all seem to survive each year
with varying degrees of health but usually regrow well in the Spring.
Has anyone grown Campanula Cochleariifolia successfully in a container?
Does it have special needs when grown in this way?