Wow this went a long time unanswered!
I am looking at the same issue.
The problem is that the files it is not finding are not in your local cache. When offline you can only get what is in your local cache.
So the setting required (probably) is "refresh cache during login", and "clear cache during logout" must be unchecked.
Then what happens is rather than just caching files yuo check out and view, when you log in the first time there is quite a wait while the entire set of PDM vault data is copied to your local cache.
Then subsequently, when you log in it will update all the local files on your cache with the latest versions from the vault.
I've just got an up to date cache to work offline on my laptop and will be checking out that I have correctly understood how this works for sure in the near future!
Now, working off line, you should only really change files that you checked out (ones that are read only to your colleagues).
otherwise you might find your edits overwritten when you log back in.
So my advice is to make a temporary local directory and put all the files you edit offline in there, if you hadnt checked them out, perhaps with their names tagged. Then you can manually update what needs to be re-introduced to your vault when you are back on line.
Stuff you checked out you can work on normally, and when you reconnect just check them back in - confident you arent overwriting any of your colleagues edits.
Something to watch out for is if you create any new parts, save them somewhere outside that offline vault system otherwise you end up with a bit of a headache. Because you will have files saved with the same apparent file path as stuff in your vault, but which is not registered to the PDM database - and which show up in your recent files but not in the file explorer. Getting them registered in the PDM database, or finding any that scrolled off your recent files, can become an issue.
I'll come back and link a another post on that problem!