You can feel presence of God during prayer.
I have prayed, in my lifetime, and not felt any different from when I wasn't praying.
If you don't believe in God how do you explain countless cases of terminal cancers being cured, or just disappearing for no reason? Doctors giving patients deadly diagnose, and patients miraculously survive and cancer disappears without a trace.
"There's no explanation for it, so it must be the work of the gods" is, I think, a fairly antiquated line of reasoning.
Just 2 weeks ago I heard a story from a guy who lost ability to speak after a stroke. In his dream an angel gave him specific day and time when he will speak again up to the minute. And guess what, he spoke at exactly that time! How do you explain that with you science?
For every person who had some sort of premonitory experience that receives notoriety, there are thousands of people who did not have visions and went unnoticed. These mystical events occur rarely enough that they can be disregarded as coincidences -- however unlikely the coincidences are, they're bound to happen once in a while.
In this particular case, I have no reason to believe that the person's story is true. I'm not claiming he's making it up; however, it's very, very common for the brain to make false memories. It happens to me with some regularity. A person who already has religious leanings is more likely to invent (entirely without the intention to do so) religiously charged false memories.
In addition, it's worth noting that this guy has suffered brain damage. Do we really want to take every experience of his as complete truth? The probability that he has had hallucinations is pretty good. And lastly, some forms of brain damage -- especially legions in the temporal love -- actually cause religious visions and feelings of being touched by God or angels.
Of course, that's not evidence that they're
not touched by angels. However, before you suggest that God reveals himself to people through epilepsy, or remind me that the Bible states that no man can look upon the face of God and live (so maybe those few who do live merely suffer brain damage, hence the correlation), I'd also like to mention that there's a device that causes people to have these visions, is non-invasive, and has no long-term side effects. Is it reasonable to suggest that God is being forced to reveal himself to people on whom this device is used?
So while there might not be a scientific explanation for spontaneous remission, there is an explanation for why you hear about them, and there's an explanation for religious visions.