In the case of most electret condensers "what goes first" is not the frequency response, but rather the ability to tolerate loud music before distortion. Loud is a relative term of course. But with a full 9V you can tolerate xxx dB's before the mics brickwall. When it gets down to 6V it will brickwall at a lower value. If you are looking for some one to tell you "as long as it's about 6.0v you are good", I don't think anyone can say that for sure.
This is what I do (right, wrong, or otherwise). If you put a voltmeter on a new 9V alkaline battery, it will probably read a bit above 9.0V, like maybe 9.5. If you run it for a few shows it will probably be down to 9.0. After a few more shows it's probably down around 8.5. The mics probably have plenty of headroom at 8.5, but that's where I tend to replace them because at some point in the near future voltage will probably start to drop like a rock, and that's the show that will get distorted.
If you aren't into voltmeters, then just replace the battery before every "important" show to be safe.