Should a VFD be turned off when not in use, as much as possible, or should it be left turned on all the time?
Typical lifetime of a VFD display is 30,000 hours, and the luminance of the fluorescent phosphor (typically 505nm ZnO:Zn) will fade as well as evaporation of the filaments.
VFD filaments run at relatively low temperature so I wouldn't worry too much about cycling, but you might want to blank the display and turn the filaments off to save power and prevent burn-in.
The delay you use has more to do with your application and whether a slight delay coming back up would be an issue. You could blank the display quickly and turn the filaments off after a longer delay if there is a noticeable lag. I think there's a perceptible fractional-second lag in starting up my 1970s-era Casio &quot;Computerized Quartz CQ-1&quot;.