"The issue is not the number/frequency of releases of Firefox, but more likely the age and oddity(?) of the extensions you are using."
That's not true. The problem is the frequent release of MAJOR versions.
You see, when writing a plug-in for Firefox, you have to specify for which versions of it the plug-in works. Of course, if you specify either a particular version (e.g., 16.0.1), or a hard diapason of versions (e.g., 4.0-16.0), then the plug-in will stop working as soon a new version is released. However, it is possible to specify a fuzzy diapason of versions - e.g., 4.*-16.*. Then if the new releases change only the minor version number, the plug-in will continue working (unless, of course, it uses something that gets broken - but that's extremely unlikely in a minor version).
However, you can't specify wildcards for the major version number and because Mozilla change the major version number of their browser so often, lots of plug-ins stop working.
In addition, Mozilla take half of forever to approve a new plug-in (or a new version of an old plug-in), so even if you update the ones you've written immediately, it will take considerable time until their new versions become available to their users.