APs can have length of stay FPs, as long as *every* single day of FP is tied to an onsite, Disney-owned resort reservation.
A single day of FP without an onsite reservation will trigger the 7-day limit.
The problem with CLFP is that the system does *not* recognize it as a FP tied to an onsite reservation. Only the regular FPs that you can book yourself at 60 days are recognized. It thinks you have an FP booked without an onsite reservation. As such, a single day of CLFP will trigger the 7-day FP limit for APs.
So, I would recommend that if you have a long onsite stay, that you avoid CLFP, as you will only be able to make FPs for 7 of your days.