Using Arduino Micro With 12V Buzzer
Attach your voltmeter across the battery, and measure the available voltage when different things are attached; or attach it in series, and measure current draws.  You probably will find that a 9V battery's voltage is under 8 volts when a mix of multiple Arduinos and buzzers is attached.  That voltage may be too low to activate the buzzer.

A powerstream.com web page called 9V Alkaline tests shows how rapidly a 9V battery's voltage drops when heavy currents (more than a few dozen milliamps) are drawn from it, and a batteriesinaflash.com web page includes the following diagram that shows battery voltage quickly falling below 8.5 V in its first minutes of life when 27 mA is drawn from it. 

For some models of Arduino, eg the Uno R3, various posts on the web list currents from 25 mA up to 45 mA, depending on LED and sleep settings.  Currents for the Duemilanove from 10 mA up are reported.  The Arduino Micros in your tests probably use a little more current than Pro Mini boards (which have no USB), and although it's unlikely they will use as much or more current than the buzzers, they still may drag the voltage down to a level where the buzzers won't work.

If your system needs to be battery powered, consider using separate batteries for different devices, to avoid problems like you saw.  Alternatively, use heavier-duty batteries, eg good-sized lithium-polymer units.  Also review posts about decreasing Arduino power usage via sleep, disconnecting the power LED, and using large capacitors to buffer power surges.

Edit: Given that voltage measurements show enough voltage being available, the suggested use of capacitors or inductors to isolate circuits may be a good idea.  

When adding a capacitor, locate it physically close to the power-using board or component.  For electrolytic  capacitors, attach the capacitor's + terminal to the high side, eg to the +5, +9, or +12 side, and attach its - terminal to ground.

When adding ferrite beads, wrap the supply wire through the bead several times, if there's room.  The picture below illustrates the idea.  

An electrolytic capacitor across a circuit acts as a voltage reservoir.  It also gives high-frequency signals an easy path to ground, reducing interference.  A ferrite bead or other inductor impedes high frequency signals, again reducing interference.