Your description suggests the documents referenced by the hyperlinks are being opened (but in the background) and, when you exit Word/Windows, those documents aren't being closed properly; that's why you get the prompts next time you start Word. I don't use SharePoint, so I can tell you why the opening behaviour is inconsistent or how it might be resolved - but at least you now know what's happening and that should help with further diagnosis.

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Cheers,
Paul Edstein
[Fmr MS MVP - Word]