Not all staterooms will hold the "max" number. Some may only have beds for 3 or 4 even if others in that category sleep 5. So yes, there is a limitation based on the number of beds. It could be there are no rooms that sleep 4 remaining on your cruise.
There is also a limit by age. So if one of your kids is an age that has reached max capacity, you cannot book.
And since staterooms may sleep a varied number of guests, some rooms may not be available even if there are unbooked rooms if the muster station is full. So it could be there is only space for 3 left in the muster station, therefore only 3 people can be booked even if a room has more beds.
ETA: I just played with the May 21st Fantasy booking, and it would seem they are no longer taking reservations for a party of 4. Either there are only rooms left with just 3 beds, or muster stations are getting full. It doesn't appear to be an age issue.