i had no problem booking the first 5 days of fast passes and still have ticket availability from a # of days perspective.
I keep getting the following error:
FastPass+ Limit Reached
These Guests have reached their maximum FastPass+ allotment. To continue, remove them from your party. Their existing plans won’t change. Or, go back and select a date for which you already made FastPass+ selections.
Make sure you only have 3/person/day- and that your ticketed days equals the days for which you’re trying to schedule
Also make sure you are only booking for one park each day.
Is it happening for everyone or just some? Are you including anyone who is staying offsite - maybe they have APs and already have 7 days worth of fps booked in the month…
If you can give us more details we might spot the problem.
I had the exact same issue. After 1 completely fruitless chat session and 3 phone calls to the Disney help center, the cast member ended up having to override the FPP system and input that individuals FPP separately. He aligned them as best he could with the existing FPP for the rest of the party (meaning the exact time frames did not necessarily match but there was sufficient overlap). I was basically told that this is a glitch with some tickets and it was my bad luck to have gotten one 
. I think your best bet at this point is to make the phone call to Disney and try to get them booked over the phone.
Good to know! Now I won’t freak out if it happens to me in a couple of weeks. Thanks for sharing!