>>As a debug exercise you might add a GUID property to your connection class and log this before some of the offending error lines. This should enable you to check whether different hits were actually accessing the same connection and, if so, might also provide a clue as to where this was happening...?
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>The GUID property is a good idea. However, when those hits are hitting the server at the same time, only one will have the error. So, even if I would have a GUID, I wouldn't be able to compare it against something.

I'd give your .oProcess object a GUID as well and log both GUIDs all the time - not just when there's an error. If you find a case of the same connection GUID being used by two or more different processes you'll at least know that the source of the problem is indeed the sharing of a connection. Logging the method as well might help to narrow down the code where this is happening. It's also worth checking the log even when there's no error - it could be that the connection is often shared without having side effects which actually cause a problem....