I have the same issue too, although i have found a mild fix for the tabbing out of a game issue. Its not a fix, but an easier way to get back into game without having to restart your client. Basically, if you tab out or the window screen is minimized for whatever (I.e battery message), just quickly open task manager (or just keep it open before you start a game), find your league client thats running. It should say its not responding (reason why you cant tab back into game). Click it once and it should list another league operation below it, double click it, and it should reopen the game for you without having to exit the client or reload the game.