Hi @Ann-And-Mad0 .
Sorry to hear you've had this difficulty. As I understand it, a guest will always be refunded any unused portion of their stay if the booking has been cancelled by airbnb.CS. Unfortunately I suspect airbnb will favour the guest in this instance. However at least you will have your calendar dates opened up for rebooking. It's a much better to have the guest leave NOW than stay on, and complain at the end of the stay and still get a substantial refund ( which seems to happen a lot providing the guest with a near free stay and the host with a big loss of income). To "cover" yourself for the future perhaps make a note in your listing re the speed of the internet ( if it is indeed a little slow)
Also, not sure how long your guests "month" was, but if the guest was staying for more than 28 days - in Australia this means he has become a TENANT not a short term renter, your cancellation policy is irrelevant. Many hosts avoid stays of longer than 28 days for this very reason. In fact many hosts recommend not having stays of longer than 1 week - 10 days as the longer a guest stays, the more likely they are to find things that annoy them and complain.
Just my thoughts. Other more experienced hosts may offer other opinions.
Regards