This looks cool! This is gonna be a Cactastic game! (Oh, look! I made a pun! Kneel before me, mortals! ;P ) But eight real time hours... That's kind of a let down, considering it's a single-player game and not MMO (although I have no idea how this minigame functions in FFXIV since I don't have it).
In FF14, it's three times per day, which was part of a recent update. Before that, it was once per day.
The chances of gaining money from the Mini-Cactpot are too strong to allow it to be accessed over and over. It's designed to be a gamble, not a method to get rich quick. There is also scripting in place to nullify bypassing the time limits by editing the time on your computer.
This video illustrates how the game functions. It works exactly the same in FFD.