You pretty much told us why. Funny things happen with removable media. They get removed, or Windows thinks they got removed, or whatever.
Copy the file from the thumb drive to your Downloads folder, work on it, then copy it back. That's what I often do.
Now for files I need quick access to on different computers, I save them in Dropbox. I have the Dropbox folder installed that syncs the files on each computer's hard drive, and this syncing is pretty quick, so by the time I walk across the office to another computer and sit down, the file is up to date.