Welcome to the joys of Disney reservations systems. I have never found a specific minimum stay requirement, but we do know from other posts here and my personal experience that there is an algorithm the site uses to show availability based on days selected and length of stay.
There doesn't seem to be any specific pattern, unfortunately. I have tried to get 7 (or 10 days) in a row and nothing, but breaking it up into 3/4 night stays shows availability for the whole time (same type of site, same dates). Others have posted where 1 or 2 days show no availability, but adding a 3rd day to the beginning or end, shows availability for all 3 days.
The system does seem to try limiting "orphan" dates, a single unbooked day. There is also likely a timing component to it too, based on experience. Lots of posts of people only able to book a partial stay, but are able to eventually add the missing days as they get closer to their trip. This could be system driven (releases orphan dates the closer to the actual date) or due to cancellations. Again, there doesn't seem to be a consistent pattern.
The best answer to add days is to book as much as you can and then check the site periodically to see if your additional days become available. Most have voiced success by checking closer to arrival date (within the cancellation window). It seems many will hold a package reservation until the 30 day mark when they have to pay in full. This would personally make me crazy, as I like to have things planned and decided much sooner than that, but nearly everyone on here that has tried adding on dates, even during busy times (Halloween, Christmas), has been able to get what they wanted.
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