I was having a debate with a Christian about coincidences versus God's intervention recently, so I'll share a few points I made.
Even if something completely unexpected happens more than once, even several times, it can still be down to coincidence. For example, if you roll a die and get a six, and roll the die again and get another six, and another, and another, you would be amazed. But there is still a 1 in 6 chance of rolling a 6 each time. Those odds don't change. You are just as likely to get a 6 as you are to get any other number. Another example would be winning the lottery. The odds against that are extremely high, yet people do win. In fact, some people win the lottery twice or more. Is God helping them, or is it just common sense to know that even if the odds of something very unusual happening are astronomical, there are still times unusual things will happen?
Then there's self fulfilling prophecies, in which people focus on the things that back up their beliefs, while ignoring other things. It's like a favourite song on the TV- you may hear it 5 times in one day, and come to the conclusion that the music channels have 'answered your prayers'. But if you were to get hold of the complete listings to all the TV music channels, you may find that several other songs were played more. The reason you hadn't noticed this would be because you were only looking out for your song. If indeed it had been played the most, it would not have anything to do with you personally. It would only point to the fact it is a popular song, and it just happened to coincide with your favourite song too.
Even if we somehow disprove other explanations, it does not mean God becomes the default answer. It may have been Krishna, or Mars, or Neptune. And while you may pray to the god of the Bible, another god may be the one who answers because people stopped talking to him or her long ago.
So in conclusion, I think with the endless amount of possible outcomes, it makes sense that on occasion, things we perceive as unusual or amazing are bound to happen.