I have exact the same problem with my Apogee Ensemble. It is great to hear that I am not the only one with this issue. Only way to get it working without dropps was to run Logic on a seperate installation of SnowLeopard on the same SSD. No way to get it working without drops and pops on Mountain Lion. Apogee support could not help at all and is pointing on problems with the OS. I really do not understand how they have tested there drivers by telling they are fully compatible with ML. I thought that a faster new iMAC i7 could probably help to solve this problem, but after reading your post, recognicing that you have this issue on a MAC PRO, I will definitely not upgrade my Hardware.
My hardware configuration is: iMAC i5 (mid 2010) with 16Gbyte Ram, 512 Gbyte SSD, 1 TB HD, Apogee Ensemble, Apogee Duett (exact the same problem btw) , Presonus Fire Tube ( working without any problem btw.) Yamaha CP1 connection via USB-MIDI-Driver. (latest driver version)
Interesting thing is, that if you change the parameter processor threads and working buffers, it seems to change for a while before it comes back after a some minutes. And it does not matter if you change the io-buffer to the next higher amount. On SL it works without problems with io-buffer size 64. On ML it does not work with 256!