I had a DMP2 for a while. Nothing fancy, but it works. I've not used a microtrack. My gut feeling is that this isn't really an issue with the preamp.
I would guess either:
a) the signal between songs drops down into the noise floor. For instance, it's fairly common for me to see signals drop to -48 or -60 between songs when hitting 0 at the peaks. If you listen closely you can hear people chatting mixed in with the hiss, in which case it's not actually a problem, that's how it is supposed to work. If your noise floor isn't quite as low as that, you won't hear the people, all you will hear is the hiss.
b) perhaps there is some sort of "noise gate", compression, limiter, or VOX setting on the Microtrack? A noise gate is a tool used in mixing to cut the signal below a certain threshold. These noise gates have their pros and cons, but the point is that if you were using one by accident, you would definitely cut out the dead space between songs. Compressors and limiters compress the loud parts but not the quiet parts. Ham radios have a VOX setting... when you want to talk you don't have to press the "talk" button, it detects that you are talking and flips to transmit mod. I believe this is common on digital voice recorders. If the MT has any of these type settings turn them off.
Try to pick a gain setting and stick to it the whole show. If you started out with the gain too high and you are clipping, then you have to turn it down, yes. But every time you touch the gain control during a show, that's an adjustment you are going to have to level out at home.