Game won't unpause after switching windows (Java 7 on 64-bit Linux)

If I switch to another window while playing Minecraft, when I go back to Minecraft the game won't unpause. It doesn't matter if I pause the game before switching windows. When I click the "Back to Game" button in the menu, the clicking sound plays, but the game doesn't resume. All the other menu buttons work correctly, and I can save and quit without a problem. I have to exit Minecraft completely to get it to work correctly again.

The bug first showed up when I upgraded from OpenJDK 6 to OpenJDK 7. When I went back to Java 6, the bug went away. Unfortunately, I can't stay with Java 6 because of MC-2749. I don't have a crash report because the game doesn't crash; it just stays at the menu forever. I tried updating LWJGL just to see if it would make a difference, but it didn't fix the bug.