My son has a similar problem with his Android tablet. The game will load but it drops out back to the home screen at various points in time and for no apparent reason. It may not seem much to Activision but £4.25 of Christmas money means a lot to a 9 year old.
There seems to be no way of getting a refund so I'm guessing that we will just have to wait for Activision to resolve the problem in their own good time and in the meantime, avoid their other paid offerings.
Whilst I'm grumbling about things, I find it hard to believe how hard it is to use the Activision support site too. The cost of my time trying to stumble around the site is more than the value of the game. Maybe Activision hope that people will just give up out of frustration.
Very sorry to hear about you and your sons issue with the game. Lets see what we can do to figure this out.
What device are you currently playing on? Are you using the Bluetooth portal with the game? What champions do you currently own?