Hmmmm, I could answer this a couple of ways. We do extended trips, but don't stay in one single resort for the entire time, but rather change resorts.
We've had a number of trips with stays of 3 weeks or longer, but technically our longest stay in a single resort before moving to another resort is only 6-days.
Our longest stay ever (so far) was a combination camping/DVC trip. Counting all resorts combined, which includes the WDW Campground and two other (off-site) campgrounds, was 11-Weeks. Six of those weeks were on site (Ft. Wilderness, OKW, BWV, VWL, BCV, OKW again) and Five weeks offsite (31 days at Campground #1, and 4 days at Campground #2)
Specifically, we spent a week solid at Ft. Wilderness, then did the DVC resorts one after the other, but only did 5-nights (Sun-Thu), and spent the weekends in between back at Ft. Wilderness. When finished with the on-site stays, we moved off site (Hwy 192 West) at an extended stay campground where we had a coupon for $99 for the month (Plus electricity). After that we finished up at another timeshare campground where we got 4-nights free camping for taking the sales tour. (we didn't purchase).
And yes, on that trip, we got very good use out of our Annual Passes...
Counting the trip down, stopping at numerous campgrounds on the way (EG Smoky Mountain N.P.), and the trip back with more stops, the entire 'vacation' lasted 14 weeks. It's great to finally be retired.... (

). I highly recommend it..