See here or he like for typical troubleshooting techniques: https://supportforums.cisco.com/thread/2131666
Problem: You find your Cisco UCCX server(s) in partial service, and after drilling down find the Application Manager is in partial service. One option is to change the trace levels to debug on the APP_MGR, restart the engine(s) or server(s) and then examine the MIVR logs. Searching the logs for PARTIAL_SERVICE or ERROR at the time of reboots can be telling as it may reference an offending script. At at high profile installations, restarting / rebooting is not a practical option, and pulling logs from the Linux appliances is not as easy as it was on the older Windows based systems.
Possible easy solution: Check the Real Time Reporting in UCCX. From the administrative GUI, choose Tools | Real Time Reporting | Report | Applications. You should find a grid of the applications on your deployment and a column on the right titled Valid.
If any of them have a value of false, you can be sure the partial service is at least partially attributable to that application. Validating the script via the script editor, checking for valid sub flows, etc. is in order.
If you don't "own" the administration of UCCX and have various administrators not checking server health after their changes, this is a nice easy option, pointed out to me by a customer in just such an environment. It appears to be available in at least versions 7 through 9.