There should be nothing preventing you from storing backups generated by Quicken on a networked drive. You can set Quicken to save a backup every time you exit. Are you trying to keep your working QDF file on a network drive? I think the issue with that is not the reliability of the external drive but the reliability of the network connection, espeially if you try to access your data file from one of those remote locations.
What version of Quicken are you running?
@tefield: My question: What would it take to remove the filter that keeps network drives from showing up?
Where are you seeing network drives filtered out? I can easily open a QDF file from my NAS.
The reason we don't recommend it is that Quicken predates home networks and has always assumed it is talking directly to a local drive. So if any network error occurs when writing the data file (which Quicken does after every change), you have to hope your network infrastructure is robust enough to recover automatically.