Partial week rentals are a loosing proposition unless the owner is desperate for income.
Also that time of the year many owners shut their houses down for the year after thanksgiving.
They're mostly a losing proposition because of how PMs execute them. If a partial rents at a pro rated amount based on the percentage of a full week, yep, that's a losing proposition. The ADR on a three night stay and a 7 night stay is what makes it a losing proposition. That's just poor execution. But, from a business perspective, it only makes a difference for the owner. PM doesn't lose out. It has made some tidy profit options for the VRBO and AIRBnB crowd, though.
Biggest problem for this group with finding a partial at Christmas is how late it is to be looking. Needing a large house doesn't help either.
Since a house that large is probably not booking as much during December as more moderate homes, an alternative may be asking to book a full week with a shifted check-in/out day. Same money for everyone, change for the cleaner, and not likely to be constrained by stays before or after.
One tip for those looking is to speak with a manager and not who ever answers the phone. This is VERY important. The manager can make an advanced partial reservation IF the manager knows the likely hood of getting a full week rental is not going to happen. At Christmas that is very likely not to rent for a full week and a manager can make an exception and reserve one for weeks in advance - if they want to, I know it has been done but may not be too common.
The biggest difference is the fee the PM adds on to a rental, that is the same amount for 3 days or 7 days, the rest is prorated.