The majority of quests in the game are repeatable, but not every single one. There are a couple of the very beginning E-rank quests that can only be performed once (possibly because they're just meant to be introductory). I think this is the full list here, but I'll double check later tonight when I can get on my PS3.
- Defeating Dogoos
- Super Strategy: Spa Conqueror
- Seeking Nep Bull
- Training Regimen
- I'll Never Stop
The first three are just -5% Arfoire, +5% Planeptune in Planeptune. Training Regimen is -10% Arfoire, +10% Planeptune in Haneda City, and I'll Never Stop is -5% Lastation, +5% Planeptune in Planeptune.
Every other quest is repeatable, though, and there are other quests that accomplish the same share effects as these ones. Just a lot more annoying than handing in all those 99 Herbs you tend to accumulate.