Here’s the scenario:
You’ve got this great document library, but you want to move to another site, under the root site collection. You save the library as a template, but when you get to the other site, it’s not available in the list of templates.

Check to see if there is a feature that is activate in the orginal library’s site that is NOT activated in the destination site. Once you’ve found that feature (or those features), activate it/them in the source site. Chances are, that will make it show up in your template gallery.