I'm wondering if I'm doing something wrong when trimming back my rosemary.

I clip the branches about midway to keep the bush more compact and dense -
but all that happens is that a few months later the entire branch dies. So
in frustration I've just let the bush grow where it may, which is pretty
tangled and sparse.

Why is this happening? Is there a specific time to clip rosemary, a
specific location on the branch perhaps?