I just discovered something that could affect many users.
BaseCamp, unlike MapSource, does not save track/trip log details (timestamps etc) in it's database GDB file (Alldata.gdb). Instead when you import (through whatever means) a track/trip log BC stores many of those details in a file or files in the TrackSegments folder.
So why is this relevant? Well if you copy a BC database to another location or machine and don't copy the files in TrackSegments you lose all the details in your track/trip logs! In short you must copy the whole Database folder.
PS: In my case I was able to restore, from a backup, the entire Database folder from a few days ago and get everything back :)