Why are you saving it somewhere else? There's no need for that, and one of the main points of using PDM. I'm guessing that it's the fun workflow of people copying all of the necessary parts into one folder. So you're probably used to having multiple parts with the same name, and the changes not being propagated to all of the associated assemblies.....
1) Set up PDM so you can't have duplicate names of parts, assy's, and drawings. This will save you sooooo many headaches.
2) If you do need to do a save as (renaming, not the location), check it in right away after the save as.
3) Learn to use copy tree. It's a huge time saver when renaming files.
Do not copy files out of the vault unless you want to create problems for yourself. Duplicate files will ALWAYS cause problems. The PDM vault allows you to check files out and open them right there for edit. No need to copy them out anywhere else. This is assuming you create the Vault View (blueberry icon) on your root C: drive or somewhere like that.
If you need to work off-line because you're traveling, then do exactly that. Go to Tools > Work Off-line. All of your green folders will turn blue. As long as you have files checked out before you go off-line, you'll be able to work on them.
Just to clarify...your vault should be located off of C: directly..don't put it in sub folder and ensure that everybody has the same path!
That's why C:\ is the preferred location. Don't make the mistake and install in c:\users\<name user> folder. That will cripple you.
Being offline means the file is not added to the vault. When you go online, you have to locate all new files and use the right-click -> add to file vault option, and then check them in.
That said, consider the other tips given in this thread.