AirBNB is clearly reaching a critical mass world wide. It's spilling out into forums like this, I heard somebody talk about it at my local REI club last week and at the building department - not to mention the nation-wide TV commercials they started airing about 6 months ago. It's a brave new world out there, and Airbnb is here to stay - and I would strongly suggest everybody who's into rental income to explore it, read their terms and conditions, talk to your attorney about it.
For the record, I am both a traditional landlord and an Airbnb host. We host people in our guest house, and my wife finds it pretty easy to manage, while I deal with the website booking and interaction. We've increased our liability coverage - I don't trust Airbnb's "million dollar guaranty", as it specifically refuses to cover medical bills, accidents and such and only pretends to cover personal property.
I also rent out a house to a young family on a year-lease - and that property has a guest house as well, and I'm monitoring and waiting for a day when I have to address Airbnb issue with them... or cure :)
The site is nothing more then a middle-man and a platform to connect hosts and guests - even though their own terms and conditions try hard to avoid that label. They are trying to be a PayPal account for short-term rentals in complex, over-regulated municipalities all over the world - and pissing off the hotel industry, a lot of finance departments and clearly some landlords in the process. You can rent a castle in the Scottish countryside or a tent under a tree in my neighborhood in Miami and everything in between.
Airbnb won't give you any info about their users - tenants or guests. The original poster will not be able to leave his "tenants-hosts" any sort of negative or a warning review until he registers on the site, goes through some form of ID check and then requests and actually completes a stay - and I doubt that's happening. Contrary to what some have suggested, the original poster can't just take over their "business", using the "good-will" accumulated by the positive 5-star reviews and use it from here on to his advantage. All of the reviews are tied to personal information of the host, not address of the accommodation - many hosts have multiple listings, and all of the reviews show up on the individual listing page, but also always point back to the host.
Clearly, the disconnect here is that you're carrying extra liability and your property is experiencing additional wear&tear - all without any additional benefit to you. That's the reason most condo HOA's don't want to deal with units that are found to be Airbnb hosts - too much liability exposure without any tangible benefit to HOA as a whole. But you as an owner of a single family or a duplex may be able to derive additional income while protecting yourself from additional liability. Short-term rentals are nothing new in RE, neither is allowing your property manager live on premises of a multi-unit complex for free or at a reduced rent in exchange for management services.
While you've already served them notices, you can still sit down and explore with them this brave new world that's you've finally stumbled upon - even if you still say no at the end.
You could terminate the old lease on mutual agreement and re-sign a new one, on terms that lay out how you see this potentially moving forward. You can reasonably demand more money form them without seeming greedy simply by explaining to them that you need to update your insurance liability coverages, perhaps get a permit or an additional license. There may naturally be more wear and tear - but there may also be significantly better maintenance on their part, as the good reviews don't come by easily and they've already been doing something right.
Very curious to see how you and they handle it, though - keep everyone posted.