Download the schematic at:
http://elektrotanya.com/mackie_1604-vlz_mixer.pdf/download.html
Scroll down to the link to download that says "Get Manual"
This is for the 1604 unit which is just a truncated version of yours. When downloaded, find the phantom power supply on page 18.
There are too many components to guess which one so best just to troubleshoot.
I would even suspect the phantom switch since they have POOR design with no inrush current limiting when charging the input capacitor. Since the 48 is not individually fused, if the inpout cap C3 shorts, it probably will take out the switch or the diodes.
Another user had the Zener D9 fail which would cause the problem. Meter the voltage across C3 (probably about 60 volts) and D9 and C4 (47 volts). First check C4 as that cap is run TOO close to the rating of 50 volts... poor design... C5 would also be suspect... or Q1 and Q2.
Then it gets dicey as there are UNDOUBTEDLY many bypass caps in the mixer portion of the board.