Dear Ask A Punk-
My neighbor is a problem. I live in an apartment building in a fairly big city. Even though I'm obviously very punk rock, I'm actually surprisingly polite and quiet and try to be a good neighbor. My band does practice at my place sometimes because we can't afford rehearsal space, but even then, we're not playing at performance or even practice levels, we're sounding practically acoustic and on top of that we schedule playing for afternoons or at some decent hour. I know I'm making myself sound like a saint, but the truth is I know I'm less of a problem than some of my other neighbors who get drunk every weekend throw parties and blast their stereos, but for some reason the woman upstairs thinks we're a "problem" for the building and she complains, bangs on walls like you would think we were the biggest problem in the world. How do you shut up a neighbor like that? - apartment dweller.
You really can't appease someone like that, especially if she has completely made up her mind that you're a 'big problem' because then you become the source of focus for alllll the anger and frustrations in that woman's life. No matter what else she is dealing with she can say "and now that goddamned band is playing too." Since she probably can't control or fix the things that are really causing her to hate her life, she has decided to focus her rage/frustration/anger on you and your band.
Even though I've been in bands I understand how it can be weirdly (and exponentially) way more annoying to have to listen to guitars and drums being played and stopped and played again ...it irks people more than a loud stereo does. It is sort of like having to sit in a room while someone else plays a video game... as much as I like a good game of Halo or Modern Warfare, if I'M not playing and someone else is, all those exploding grenades and bursts of gunfire get on my nerves almost immediately.
So it sounds like I'm completely taking your neighbor's side, but trust me, I'm not. One of the deals we make, being city dwellers and living in warrens of apartments IS that we're going to be impacted and sometimes inconvenienced by our neighbors in ways we wouldn't be if we lived in a house in the middle of a corn field. Obviously she has to figure out how to live with you, especially if you're doing your best to minimize the noise and inconvenience to her. I'm sure you've pointed that out to her in terse little conversations by the mailboxes etc. As I said earlier, you're probably just the latest scapegoats for a life she isn't enjoying, and a part of her just likes to hear herself complain... otherwise you would have told me that she had also complained to the landlord and/or the cops... If she hasn't then she probably KNOWS that they would tell her she's a crackpot... so take that as some consolation.
I know the younger and more hardcore punk rock folks would say "Screw her" and just turn the amps up and reallllly give her something to complain about. I certainly understand that temptation... but that only works if your goal really is to make her life (and subsequently yours) more miserable. I suggest you keep the moral high ground... keep the volume low and your exchanges with her as polite, brief and infrequent as possible. It would also help your case to make sure you know and are friendly with as many of your OTHER neighbors as possible... because sooner or later, she IS likely to go to the landlord or the cops and the first thing they'll do is survey the other neighbors to see if this woman's problem with you is valid or not... so it would be best to have as many allies as possible.
...and the next time you put out a new song, dedicate it to her.