Dock Connector Problem

I'm having a peculiar problem with the dock connector on my iPad 2. About a month ago, the connection started to become a little bit unreliable. I'd have to put the cable in a few times before the iPad made the bleep and either initiated a sync (if connected to a computer) or charged (if on the power brick). I have a number of dock cables from iPods and iPhones over the years, I tried all of them, in several computers and chargers, and they all show the same problem. In contrast my iPhone functions perfectly in all of these situations. This suggests to me the problem is probably with the iPad's dock connector port. So I took the iPad down to the local Apple store, explained the problem to the genius there, he got a laptop out with a dock cable, plugged it in, and it worked perfectly, first time. So now I have an iPad that is nearly out of batteries with not way to charge it or back up or sync it. It's a bit of a journey to the apple store from here, so I don't particularly want to come back with the same problem just to find that it works fine for them again, I'd like to know if anyone has any further suggestions of things I might try at home before making the journey.