Ok, I'm confused, just store the PST elsewhere. The location can be changed.

Sounds like he should make a copy to dropbox, if he wants a copy backed up.

Can't backup an open file after all.

This is just how computers work.

He is not complaining that the file can or cannot be backed up, and Dropbox is no backup service by the way.

He is complaining that their software hangs on open file instead of doing the sensible thing and not using 100% cpu until the lock goes away. That has nothing to do with "how computers work".