How are the computers networked together - wired only , wireless, mixed ?
Anything different about the "one" ? OS or patch level ? All machines the same ?
What software / hardware changed on that machine before this started ?
The windows installed software + updates control panel may give you an indication if there was an update installed just before related to the network hardware.
Which NAS and software version is running ?
It sounds like either a time out issue or a name resolution, perhaps discovery issue.
If it is wired connection, does the problem move with the wire ?
If wireless, has anything changed in the physical path to the access point ?