iRULE Persistance Timeout Values

Do I understand your statement correctly? If so, then we don't need indefinite. We just need to set it to a higher value (say 24 hours).

You have to "touch" the persistence table entry periodically, which either means some form of persist operation (i.e persist, persist lookup, persist add), which would likely do in each request and/or response. The timer is based on idle time, so the counter restarts after each access.

Do you know what the maximum integer value can be for this variable?

I don't believe there is a maximum value, though 86400 seconds (24 hours) would not be unreasonable.