I guess it happens when I close the game and then reopen it. I only find out that it happened when a creeper explodes and destroys nearby blocks (I always set mobGriefing to false).
It happened twice, after the first time I created a new world thinking that maybe one of the mods disabled cheats. The second time it happened was after I removed some of the mods. None of the mods I have/had downloaded turn cheats off. (So, I guess, it has something to do with adding/removing files to/from the mods folder?)
I found that a temporary fix is opening the world to LAN and enabling cheats, but it's annoying to repeat this every time I open the game.