Hi Duke Leto,
every mission in P4, no matter if offered in the tavern, the guild, the townhall or demanded by the sovereign has the following parameters:
1. display duration = number of days it is available after appearing
2. mission duration = number of days within it has to be completed after appearing
3. idle time = number of days it could appear again after appearing last time
4. max count = number of missions of the same kind possibly available at the same time
5. min rank = players rank necessary for appearance
Knowing this a precise appearance frequence of sovereign missions cannot be predicted but checking every 7 days should be fine (maybe six is more secure) for almost all sovereign missions have a display duration of 7 days (none less).
Anyway, in the end (-game) this knowledge does not really help against one of the most annoying circumstance in P4 (don't get me wrong, I still love it): the frequence the landlords pleasance is decreasing increases with the number of peeople living in the Hanse/region.
So, in a big Hanse, and yours is quite big in this terms, it becomes more and more difficult to keep those piggishly, so called lords, satisfied.
If you need a happy landlord to release a road or something else needing >90% happiness let him successfully siege and plunder a towns treasure. He will be so happy about his success that it becomes easier to bribe him with "missions" - means his happiness is "reset".
And if this town is under your control: make sure that the town treasue is empty because, yes, these blue blooded fools are so geery that they even steel debts.