Is there a way to find out WHERE exactly the Code Insight/Code Completion compiler is failing?
Not readily, not without debugging the IDE.
Does the IDE keep a log of on-the-fly parsing/compilations anywhere?
No.
I suggest that you install Andy Hausladen's IDEFixPack. If that does not help then use your revision control to isolate the code change that causes the problem. And find a different way to write that code that happens not to bork code completion. Trial and error is likely to be the most productive method here, much as I hate to say that.