I too think that it should say something in your listing if you want to do that. And if there is nothing in your listing then you shouldn't go in at all.. I also wouldn't scheme on excuses why you want to come in, its best to give legitimate reasons or at least something that's believable. Saying you want to come in on a weekly basis to do things like checking the smoke alarms, or checking the supplies or change the linens will make them think that's bull**** excuses and you must think they are up to no good. Plus what happens if they say I will let you know if the smoke detector starts chirping or when they need supplies, or that sleeping on sheets longer than four days doesn't bother them, are you going to insist on it? because that can only end bad. I would put something in my listing that said how things in houses break and in order to minimize the affect it will have on a guest stay the issue needs to be addressed as soon as possible. Therefore you will need access into the house on a weekly basis in order to do a quick walk through to check for things like water leaks or frayed wires. Then I would even throw a quick reminder in their confirmation email. That way everything you told them is true, and the guest will see that your asking everyone and not singling them out, which is what they will think if you show up one day and say you want to come in and check the house.
The thing I am having a problem with is why you would feel the need to check on the house if nothing was said or done to make you think that you needed to do that. Have you had guest in the past that made you feel that its necessary or do you just have no trust in people in general?
And why just on month or longer stays? if a person will do something when staying a month they will do it on week long stays as well..
And last but not least, going through the house weekly is bound to result in embarrassing and uncomfortable situations , someones going to forget they left their under garments on the floor, or maybe left something out that they dont want somebody to see or they have a sink full of dishes or that they are just all around slobs. Your going to see something that will cause them to be embarrassed which should at the very least cause you to be uncomfortable and make you want to leave whether you checked the house or not.
I myself think unless given a reason to think otherwise its best to give the guest the benefit of the doubt and assume they won't be anything other than responsible adults. Plus if something cant be found, the first thing they are going to think was that it was stolen, and since you were in the house checking smoke detectors your going to be the prime suspect. I myself dont want to go into the houses when guest are staying unless I have to.