A miracle is a hard thing to prove. It could just be something that we don't understand.
I know of people who claim to have claimed to be healed. The problem is, all I know is that they were prayed for, and were better at some point. That doesn't necessarily prove there's a God... it could show that psychology has a big influence.
My big problem is that, if God is willing and able to intervene to heal some people, then He could just appear to us (perhaps as a spiritual Jesus), and prove that he exists as best he could. But even though it's apparently very important to believe, he still doesn't bothered to convince us he's there.
Also, God only seems to heal some people sometimes. Many times people are prayed for, but aren't healed. If I could heal them, I would do it... but the loving God doesn't.
I can see why miracles are convincing to believers. I used to believe, and I found miracles to be convincing. I used to tell my non-believing friends about it, but they didn't find it all that convincing. I found that strange at the time, but now it makes sense.
To claim that some event is the action of a divine Lord of the universe is a big claim, and miracles just don't prove that. Something amazing happening, that we don't understand, could just be something we haven't figured out how it happens yet.