The Speedrun Manual of Miss Witch

Such a min cap doesn't exist. It has no reason to exist. There's no indication it might exist. The system will offer a date for future simulation, that is not after the esimated "Fated Death" (where Ciel would live her life normally without doing further simulation, nor trying weird shit because she would know she's in a simulation). This is the only factor that the system consider.

If Ciel decide to be excessively reckless in seeking death in the simulation? The system will not precalculate when she would die before running the simulation. She can get the information after she pays up, be dumped at the point of death rather than the designated time of simulation, and do her best to make sure the Fate points aren't wasted (that's what happened here, though of course dying only a bit more than half an hour before the designated time wasn't a huge deal).