Colin, what was you longest run before you half marathon?
Although you are a bit faster than me, I suffered from the same problem at the begining of this year where my pace dropped in the last few miles. But since I trained for a marathon, having to run long runs of 18 and 20 miles, the half marathon I did yesterday I finished at the same pace as the start and managed a PB.
Maybe you need to do a few steady paced endurance runs in training.