Although I could see having a "monitoring mode" as an option, I do see the issue with people forgetting it's on or in a more practical real world scenario falling asleep while it's on, I would assume one if the reasons this feature hasn't been added yet would be battery issues like this.
There are a few things you could do to get around this issue without draining batteries as much, but would also introduce the pain of adding new features that go along with it.
1.You could have a monitoring mode, but the audio and video could have separate timeouts. Most people don't need to view video consistently for long periods unless there is a disturbing noise they want to check out. The video could have a timeout between 10s - 5mn, but the audio could have a timeout between 10s and infinity. I would assume with most cameras the audio would require much less battery than the video.
2.Increase the amount of time for live view, but also add audio alerts base on sensitivity similar to the motion detection. (this is all assuming the hardware can detect this without significantly increasing batter life.) You could even have an option if your listening in audio only mode that if an audio detection goes off it automatically shows video.