Hi anava
One way I can think of is that you simply disable the App in which your saved searches / alert are located during the maintenance. This way the saved searches are not run any more and you will not get any alerts. After the maintenance enable your App and everything will be back normal.
If your saved searches are not in another App then the Search App by now, this would be a good opportunity to move them into one. Because you shouldn't disable the Search App!
Also there used to be an App where you were able to mark host for maintenance so you will not get spammed by alerts....but sadly I cannot recall the name of it 😞
cheers, MuS