It is quite ilterally RNG :(
When you rank up, you of course unlock new quests and repeatable quests, and also when you rank up, the system assigns you repeatables to do for the day. But sometimes the system chooses quests that you've already done, so you miss out because the system didn't assign you the newly available quests.
To try to explain it a different way, and hopefully a little better: Say rank 1 has 3 quests available (Quest A, Quest B, Quest C). Rank 2 has 3 more qhests (D, E, and F), and rank 3 has 3 more (G, H, and I).
You're almost maxed out on your previous rank (rank 2), so you do the quests available to you for the day which just happens to be quests D, E, and F. You finish them and you rank up! You do the main quest to advance your rank, and you head back to your island to see what new quests you have since you're now rank 3. BUT I'M AFRAID I'VE GOT SOME BAD NEWS! The system has decided that your new quests for the day are going to be D, E, and F, even though you have access to Quests A, B, C, D, E, F, G, H, and I and you've already done D, E, and F. Someone else doing the exact same thing as you (rank 2 and doing quests D, E, and F) rank up and the system decides they get access to quests A, B, and C. So they're able to do 6 quests for that day while you're stuck at 3.
SE knows its a bug and they've mentioned it in the 'Known Issues' list of the patch notes, available http://na.finalfantasyxiv.com/... ...
Known Issues: "An issue with the Vanu Vanu Beast Tribe Quests wherein, when a player's reputation with the Vanu Vanu ranks up and the list of next available daily quests is updated, quests that have already been completed that day become selected again."
SUPPOSEDLY they've fixed it.. as their hotfix post posted here: http://forum.square-enix.com/f...
The people who are higher rank than you got lucky the first day or two before SE fixed it, and you got unlucky :( When you rank up, you're supposed to have access to 3 new quests. Some people weren't getting that because the system chose quests they already did for that day..