See also the Mozilla topic on extension signing, in the FAQ section:
- How do I get my add-ons signed if they are hosted on addons.mozilla.org (AMO)?
No action is required. We automatically signed reviewed versions of all add-ons currently hosted on AMO. All new versions will be signed automatically after they pass review.
It turns out that many of the signing issues seem to be related to cleaning and/or protecting software like CCleaner and BleachBit. Other problems that might cause an add-on to be disabled are a corrupt add-on registry or some sort of caching issue which might also be caused by the aforementioned cleaning software. Some users reported that setting the Firefox option xpinstall.whitelist.required (about:config) to false and re-installing the add-on resolved their issue.
If you have issues with this add-on being automatically disabled and you are using cleaning software try playing around with the browser related cleaning options. If this does not help or you are not using any cleaning software you might find some solutions on this Mozilla support page: https://support.mozilla.org/questions/998008
You can easily see if this add-on is signed by examining the folder of the installed extension. First locate the profile folder, see here on how to do that. In the profile folder, navigate to extensions\firstname.lastname@example.org, here you should find a META-INF subfolder with the following 3 files: manifest.mf, mozilla.rsa and mozilla.sf.
If the META-INF folder or any of its files inside are missing Firefox will regard the add-on as being unsigned. So either the add-on was downloaded from an untrusted source or some or all signing files were deleted (cleaned) at some point after being downloaded from the official Mozilla repository.
Technical info about the signing files: how-mozilla-signs-addons