Welcome to the forums Dr Kev. In regards to the ill effects of storing bottles of rum there are several threads. Look near the bottom of the page and you'll see a list of similar threads.
The short answer is that the rum was probably well sealed or it would have tasted flat. It might have lost some alcohol but it sounds like the bottle isn't going to last long enough for that to matter.
After looking below this thread I noticed that there weren't any applicable threads generated by the forum software. So here's a thread about the
effect of rum in a bottle.