Finally we where able to debug the problem and we had to use a network sniffer to follow the HTTPS connection flow. The problem was that at some point after the latest iOS upgrade the iPad did not work well with the server side encryption algorithms we had defined, and the HTTPS negotiation didn't go all the way through.
Changing the server side to newer algorithms (and disabling the older ones) did the trick and after that all is working ok.
It was quite difficult to manage this, but we where able to replicate this solution:
Basically it's about putting a computer between the network and the iPad to sniff the network packets. We didn't use a computer tho, we just connected to the communications switch to see the traffic and redirected the port traffic to the one where we had Wireshark installed (http://www.wireshark.org/), but I guess this is not common solution for everyone.
I hope this helps if anyone has the same or similar problem.