How do I round trip through premier without losing audio volume?
Premiere doesn't change the audio levels (volume or db) by default. So I'm not sure why you are experiencing loss in volume. 

My guess would be that you have turned down the audio levels in premiere by accident. Or that you are incorrectly comparing the files (have you checked the waveform to see if they are different levels?). 

If you changed the audio levels you either did it on the track, clip, or audio mixer. To check if you did it on the clip you can right click on it and check out the audio gain. The mixer settings should all be 0db by default. For web delivery I tend to keep max peaks at - 6db.

If all else fails than you are experiencing some sort of bug. You could always try adjusting the levels of the clip through the right click - > gain way on the clip.