I have had a lot of experience with "extended stay" guests. My longest was 18 months and from this I learned:
1- This would not be true of all guests, but I had a lovely young man and when he left all the linens had to be replaced because he did not wash them properly and everything was white was grey. So, either you need to stipulate that you will provide fresh linen weekly, or teach them how to wash (usually falls of deaf ears) or require they provide their own linens.
2- The longer a guest stays the more they forget 'house rules' so it is best not to overlook any transgression and communicate immediately. I have a 'no unregistered guests on property' rule to prevent ... and yes, I've had male guests bring prostitutes home (they are not in my house, but in a detached guest house, or the party that just starts with a couple of people then grows, or the friend that becomes a roommate. Not an issue with most tourist or short term guests because they generally do not know that many people, have limited time so are out and about and for a few days anyone can be on best behavior.
3- I now have a rule that they can NOT use my address for mail or anything, and refer them to the closest Private Mail Box Service and the local Post Office with info on getting their own address. So, unless you like endless reasons to contact former guests and arrange for getting mail to them this is important. I've had car registration arrive 4 months after guest left, numerous packages usually within the week after checkout, but as long as 6 months later.
4- Cleaning: Airbnb only allows us to put in 1 cleaning fee rate. I wish they would change this because a guest that stays 3 nights does not require the same time, use of supplies, or possible damages as a guest for 3 months does and it feels unfair for the 3 night guest to pay the same or for the 3 month guest to get off easy while to host either pays more (I have a pro-cleaner) or spends more of their time getting it clean. I now have a policy that extended stay guests must agree to and pay for my pro-cleaner to come every 14 days, and the fee must be paid in cash at the time of checkin. This has worked out great. Just be sure you make it clear before they book and I always calculate the number of cleaning dates and the fee based on the dates they put in and give that amount to them before they confirm the booking.
5- Payment: Airbnb will collect the funds every 30 days, but be prepared that for long stays several things can go wrong with payment. The guests credit card expires, exceeds their limit or was lost/stolen and they forget to update Airbnb. Usually it is an innocent oversight and corrected in a few days, but you need to be on top of it both by informing the guest that payment has not shown up so they can check with Airbnb, and you need to let Airbnb know from your end because these things are automated and I had 9 days go by and when I called Airbnb they had no clue. So do not wait because the problem will take a minimum of 24 hours to fix and if the guest is out of money then you will need to go through the eviction process if they don't leave.
6- So, you also need to be aware of the laws that change your guest from 'guest' to 'tenant' and if in your city that is 30+ nights and your guest is staying 2 months then you should have them sign a month to month rental agreement at the time of checkin so all your bases are covered.
7- Extended stay guests are almost always in the real-life-living mode and not tourist or guest mode, so if you prefer your peace and quiet and guests basically in for sleep and shower then you may not enjoy extended stay guests especially if they work from home (very common in my experience), make friends, enjoy playing their music loud on days off, don't pick up after themselves or have a vastly different food intake... think a vegan living with a beef-eater, or the smell of kimchi (Asian) can make some people ill, or you mostly steam food and eat cleanly then have a guest who is contantly frying and splattering oil.
So much more to consider with extended stay guests, and even more so if they are in the house with you opposed to a seperate guest house or the host being gone, and for this purpose it's even more important to fill out your "host profile" and be accurate about like, dislikes, hobbies, lifestyle, etc.
Like all aspects of life there are advantages and disadvantages to everything and extended stay vs short term is no different, it's just a matter of which meets your needs best and contributes more to your happiness and well-being because a happy host generally will have happy guests.