If restarting the Domino server helps, that suggests that this is a memory issue. I suggest you check how much memory the Domino server processes are using, and how much disk activity there is. CPU utilization is not the only important factor.
If you determine that there's a memory leak, figuring out what's causing it may be tricky. Knowing which process owns the excess memory will help. Possibly, as an interim solution, you could address the issue by restarting just that one process every couple of days, rather than the whole server.
However, this one application that's getting slow may well not be causing of the problem. Possibly there's a general server slowdown caused by another application or process, and you only notice it in this application because this is the one that places the heaviest demands on the server.
I would also look for any agents in any databases that process large numbers of documents. Are they using the Delete statement (in LotusScript, or recycle in Java) to remove NotesDocument objects from memory? If you don't do this, the objects are cached in the agent manager's memory and can accumulate over time.
Also look for any processes that delete and create large numbers of documents. I'm not sure this would cause the problem you're seeing, but I frequently see large databases that are reloaded nightly by deleting and recreating all documents from some outside data source. This can cause severe performance issues.
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