There are a number of spells that normally have a 24-hour duration, but can be made permanent by casting them on the same target every day for a specified number of consecutive days. Examples include arcanist's magic aura (30 days) and private sanctum (1 year). They all include a wording similar to
Casting this spell on the same spot every day for a year makes this effect permanent.
The logical implication of this clause seems to be that the effect becomes permanent once it is maintained continuously for an extended period. However, interpreting it in this way leads to some pathological issues. For example, if I cast private sanctum at 1:00 PM today but wait until 1:05 PM tomorrow to cast it again, there will be a 5-minute window tomorrow where no private sanctum spell is active. So, to ensure continuity, I either need to cast the spell every day at precisely 1 PM, or in the absence of precise timekeeping technology, I need to leave a safety margin by casting it a little earlier on the following day, say 12:55 PM. However, if I keep doing the latter, the casting time will be pushed earlier and earlier, until I'm waking up in the wee hours of the morning to cast the spell, and eventually even having to cast the spell twice in one day. e.g. at 12:05 AM and 11:55 PM (assuming you consider midnight to be the point of transition from one day to the next).
Given all this, does the requirement of casting a 24-hour spell on consecutive days imply that there must be no "gaps" between the durations of consecutive castings, such that the spell's effect is maintained continuously for the entire "setup period", or is it ok to have gaps, as long as the spell is cast at least once each day?