Many home owners here avoid short term (monthly) rentals like the plague. Too many problems involving property damage, disruption to neighbors, unpaid utilities, etc. which is apparently more common with short-term rentals. For this reason, home owners would prefer just letting their property sit empty rather than take on this risk.
Condo's and villa's are a dime a dozen for weekly and monthly rentals as I'm sure you already know, but if your stuck on a house then your best bet is to continue working directly with the larger agents in the area. Maybe something will pop up.
Good luck!