This is a good thing to know, as it could happen easily to anyone working with audio clips and tracks in Ableton Live, especially for DJ or performance purposes.
There are two levels of quantization in Ableton Live — with quantization here concerning audio loops we mean when there’s a certain time interval when a loop should start, 1/16, 1/2, one bar, four bars, and so on. Four bars is really the easiest way to start loops when DJ:ing, you can’t go wrong with starting a loop, and the system waits until four bars have played, and then the selected loop starts.
Now, there is a global quantization level that you set either via the menu/keyboard shortcuts and/or the player toolbar on the top. And there is also a loop-specific quantization level.
The loop-based one, see image above, overrides the global one. This means that if you deliberately, or by mistake, have this set, then the loop you start will not honor the global values. Most likely, as in the image shown, with a 1/16 bar quantization you could easily go out of sync when starting the loop.
You could change the loop-based quantization level to global, then the global value is always honored. I use this, as I rather specify on the fly what quantization I want when doing DJ work, rather than hard-wire it into each loop. There are exceptions, if you want staggering effects or something similar, you could select loop-based quantization for specific loops. Otherwise, best still to a global value across all loops. Less mistakes this way.