One of the responses I have had from a few Christians to my deconversion story can be summarised like this:
"If you had experienced God like I have experienced God then you would believe too."
Yet, I have experienced similar things to the people who have said this (and in some cases in exactly the same places or organisations). I just seem to have interpreted them differently. Rather than looking for unlikely supernatural explanations I have tended to look for more obvious explanations based on reason and knowledge of how the world works. For example, the person whose life has been transformed by prayer, might have just found the confidence to turn their own life around, or the person healed of a gammy leg might already have been a lot better, but just needed the confidence to stop using a stick.
I think this is where the argument for the existence of God based on experience falls down. The whole thing is subjective and cannot be tested objectively.
There is also a certain element of over egging the pudding by Christians. I knew one person who had to go and have tests for cancer, was prayed for and found not to have cancer. This was proclaaimed as a local miracle when, in fact, she had never actually had cancer. The doctors just wanted to investigate it further because they were concerned about her condition.