I personally don't see any problem with re-connecting. I would suggest keeping any messages short, being courteous (goes without saying!) and having a clear goal in mind in terms of the purpose of your message. Be prepared that some people may not reply - this is no reflection on you, it just means that they're busy or haven't checked their LinkedIn.
At the end of the day, LinkedIn is a networking tool, so there's no harm in exploiting that feature. I did this when I was going through the application process and generally found people to be receptive and helpful.