If there are several Mesmeric Orbs on the battlefield (3 or more) and later in the game when each player has 15-20 land in play, Mesmeric Orbs will resolve 60 or more times. While resolving, the player will start a time out even though they are incapable of doing anything. Looking at other entries, this seems to be the case with things like Scute Swarm and adding counters (anything that can resolve dozens of times at once).

Also, I noticed that after this happened and caused me to time out completely (skipping my turn once the stack resolved), when my opponent encountered the same issue, it was me that started timing out again, not him.