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I've got very regular crashes through the Adobe Air Client.
Recently I discovered that if I activate Gamebooster (v2.3) http://www.iobit.com/gamebooster.html they don't occur anymore.
Probably one of the deactivated services/apps interferes with Adobe Air somehow, maybe Riot can investigate further.
Give it a try, I hope it works for you too
P.S. @Riot: I gladly accept RP as compensation for my enormous endurance and effort to investigate this issue