Wait what? This game actually has a limit on the number of duties you can do in a period of time??
Yes, 100.
ONLY dungeons count towards this number (It's perfectly fine to do over five hundred guildhests or a thousand runs of Deltascape V3.0), but if you reach it, you're unable to do ANY content that uses the Duty Finder Queue interface. This includes other Dungeons, as well as Trials, Raids, Alliance Raids, Savage Raids, Ultimate Raids...
And then there's things that still use the interface like the Leap of Faith and Air Force One GATEs, Triple Triad Open Tournaments, Eureka, Bozja, and The Diadem, Variant and Criterion Dungeons, Deep Dungeons, Ocean Fishing, Chocobo Racing, and Doman Mahjong.
You're still able to do things in the overworld and world transfer if you're in this state, and you're actually able to go into Map Dungeons.
I'm not sure if you can do quest battles and i don't want to answer that question.
It's almost impossible to reach this limit under normal circumstances. Often you'll only see it if you're intentionally speedrunning that number (The Vault Gil Farming w/ Blue Mage), accidentally speedrunning that number (Spamming Aurum Vale for Zodiac Light), or doing things you shouldn't be (Oldschool Gil Farming in The Wanderer's Palace).
Pretty sure I'm the first person to reach it from Prae and nothing but Prae.