This has started happening since the 1.9+ releases. I'm not pressing any keys; I even did a test to see if it did it without me pressing any keys - it did it anyways. I counted and it has a delay of a minute and 15 seconds.
It doesn't have to do with breaking or placing blocks, whenever you do anything after the delay, even standing still doing nothing, you will still get the game menu. I have tried updating java and restarting. I don't have Google Chrome open or anything except the game and sometimes Firefox.