Hi Leila,
How many days a week is the guest looking to stay in the month? Would you have time to clean, etc... for another guest between the first guests stays?
If not, how about working how much it would cost the guest for the number of nights they wish to stay over then month and then send them a special offer for the whole month at this price. This way you get the reservation made for the whole month, they have only one booking/cleaning fee and they could leave clothes, toiletries, etc... at the property between stays. Everyone would win!
If you are offering this flexibiloty though, I think it is only fair that you get to set the cancelation policy to Strict before making the offer. This way, you would still get 50% if they pull out in the week before they are due to stay.
I hope this helps - perhaps not if they are only looking to stay a couple of nights a week!
Darren