Brown needles on mugo pine

There could be any number of reasons but if it is just the one branch and the rest of the tree is showing healthy growth, I would just remove it. Check your pine occasionally to see if anything else dies but otherwise just chalk it up to a quirk of Mother Nature. Branches do occasionally die for no apparent reason.

Thanks for the reply. Could it be in need of fertilizer?

There are fertilizers for evergreens but the one dead branch was not caused by lack of fertilizer. You say there is nice new growth on the shrub so it must be doing okay.

how often and what fertilizer would you recommend for my mugo pine trees

Before doing any fertilizing, do a soil test noting that you are growing pines. That will make a difference. http://soiltest.cfans.umn.edu/