Do certain sites cache listings of open directory. Maybe only capturing results every couple weeks or months or perhaps longer?
Google has a feed to the open directory but I’m not sure what that refresh rate is. Regardless, DMOZ isn’t what is used to be. These days you’re better off using your time to generate quality backlinks with other blogs.
Its not a feed.
DMOZ produces a weekly or so rdf dump http://rdf.dmoz.org/
Downstream users are free to use this dump or parts of it to create their own directory, provided they give the correct attribution.
Google is just one of ~3000 sites that use the dump for their own directory (it was ~3000 a couple of years ago when I looked at it, but is probably less now).
SOme of these directories have not used the rdf dump to updte for years, somedo it every week; Google does itevery 3-4 months - but has gone 9 months between some updates.
Thanks for the correction. 
Thank You cbp, quite helpful.
…Google does itevery 3-4 months - but has gone 9 months between some updates
At the minimum then I’m looking at about 10 wks for Google.