Two problems are happening: one, when I slide to answer an incoming phone call, the call drops immediately. Two, when my call is in progress the connection drops.
A little more info might help people help you with your issue, so..
Does it only happen in one area? -> really terrible service
What phone company do you have? -> they might not have wide coverage
Did you update recently -> 9.3 bug
Is it an old phone -> old phone needs replacing
That sounds like a bug so...Have you tried hard and soft resets? Those might help.