I have a newly built UCCX HA cluster which has been running for a week now all ok.
Now it looks likely someone has done some changes but know can find what has caused the Partial Service on the application Manager. The system is very busy so the MIVR logs are rather large.
What is the best way to trace which script/appliaction is causing the partial service error?
If you don't have a huge number of applications, just open each of the applications.. Usually, you will get an error for one of them. Especially when you upgrade from early version of UCCX, the script naming convention of 8 is different than previous versions on windows platform. I have seen customer using  in the script name worked fine under windows platform. But not on Linux platform.
Brian is right.
You'll definately see the cause of partial service in MIVR log. And it's not even a hard log to read.
If you want a quick check take a look over the scripts and do a validation on each of them see if it throws any errors.
For exemple, I had a problem once with a redirect step being incorectly configured (some number missing) and the script was working but application was in partial service. Found it in the logs.
If it's a script that has taken you into partial service you can also use Tools > Real Time Reporting to see which application isn't valid. There will be a menu with Applications as one of the options after the Java applet loads. Whichever one shows false has the bad script.