hi, the url seems alright - can you try to replicate this behaviour when you launch firefox in safe mode once? if not, maybe an addon is interfering here... Troubleshoot extensions, themes and hardware acceleration issues to solve common Firefox problems

in addition you appear to have a user.js file present in your profile, which is often a sign for adware on the system, so please run a full scan of your system with different security tools like the free version of malwarebytes and adwcleaner... Troubleshoot Firefox issues caused by malware

Thanks a lot for your help, philipp. The issue persists, but may well be too laborious to resolve. Still, here's what I've tried, and if you have any further suggestions off the top of your head, I'd gladly look into them. Otherwise, I can update manually or in safe mode (or refresh).

• No problems in safe mode, i.e. "About FF" finds the update, and I see the XML node when I browse to the update URL. (I feel rather stupid for not having tried this before.) However, just disabling all extensions doesn't do the trick.
• The user.js had been created by a malicious extension called "Youtube Unblocker". Then, recently, the extension was blocked by Mozilla [1], and (silently) uninstalled from my profile. The uninstaller appears to have reset the pref values in user.js, e.g. extensions.blocklist.enabled back to "true" instead of "false". I verified that the prefs were also reset in prefs.js. Long story short, I've removed the user.js now to be on the safe side. I find no reports of Youtube Unblocker interfering with FF updates.
• No results from Malwarebytes and Windows Defender.
• I had deliberately not updated FF for more than a year until I installed FF 44 last month. I already had to update manually then, but thought that this could be due to the switch from 32 bit to 64. I might've done something a year ago to prevent update notifications, but the user-set prefs I have now look innocent, and toggling them doesn't help: app.update.service.enabled;false| app.update.migrated.updateDir;true| app.update.disable_button.showUpdateHistory;false| app.update.auto;false

[1] Gizmodo news item: http://www.gizmodo.com.au/2016/03/firefoxs-youtube-unblocker-add-on-removed-by-mozilla-for-bad-behaviour/

ok, thanks for that information - yes youtube unblocker maliciously tried to prohibit updates in various ways. i think it places an extension in your profile intercepting pings to the update server & this extension is hiding itself from the addons manager as long as it is active...

please go to the firefox menu > addons > extensions & see if one of those entries is not showing up during normal operations:

• Adblock Plus 2.7.2 ({d10d0bf8-f5b5-c8b4-a8b2-2b9879e08c5d})
• Autocopy 1.0.8.1-signed ({0FED7D55-65D4-47b6-A6DE-9A4ADB55355F})
• CacheIt! 2.0.3.1-signed ({98449521-9320-4257-aa35-9e1a39c8cbe0})
• Check for Updates in Help Menu 1.1.1-signed (helpupdate@dagger2-addons.mozilla.org)
• Classic Reload-Stop-Go Button 1.0.3 (crsg@ArisT2_Noia4dev)
• Classic Theme Restorer 1.4.9 (ClassicThemeRestorer@ArisT2Noia4dev)
• Clean Links 2.7.1-signed ({158d7cb3-7039-4a75-8e0b-3bd0a464edd2})
• Cookie Monster 1.3.0.0 ({45d8ff86-d909-11db-9705-005056c00008})
• Disable HTML5 Fullscreen Alert 2.0.0 (jid1-Duz06d3mQhPItw@jetpack)
• Element Hiding Helper for Adblock Plus 1.3.7 (elemhidehelper@adblockplus.org)
• EPUBReader 1.5.0.8 ({5384767E-00D9-40E9-B72F-9CC39D655D6F})
• GlobalFindBar 1.0.1-signed (jid0-GlobalFindBar@jetpack)
• Google search link fix 1.5.3 (jid0-XWJxt5VvCXkKzQK99PhZqAn7Xbg@jetpack)
• IDM integration 6.25.11 (mozilla_cc2@internetdownloadmanager.com)
• Image Zoom 0.6.3.1-signed ({1A2D0EC4-75F5-4c91-89C4-3656F6E44B68})
• Menu Editor 1.2.7 ({EDA7B1D7-F793-4e03-B074-E6F303317FB0})
• NoRedirect 1.3.2.13.1-signed ({c1970c0d-dbe6-4d91-804f-c9c0de643a57})
• NoScript 2.9.0.10 ({73a6fe31-595d-460b-a920-fcc0f8843232})
• Restart Button 0.1.5.1-signed (restartbutton@strk.jp)
• SaveAll! 0.5.1-signed (saveall@ns.ba)
• Search Notifier 2.7.6.4 ({fe8d320b-2411-4e07-9c3d-f156c4a378d4})
• Smart Referer 0.0.11.1-signed (smart-referer@meh.paranoid.pk)
• Tab Mix Plus 0.4.2.2 ({dc572301-7619-498c-a57d-39143191b318})

(probably Search Notifier 2.7.6.4)

afterwards start firefox into safemode again, where it should be possible to uninstall this one malicious extension.

I've removed Search Notifier and FF updates are working again. I assumed that the hidden extension had been removed or disabled along with YT Unblocker. Also, the clean-up guides I found said that the hidden extension was called "Adblock Converter". The only two Google hits I get for YT Unblocker and Search Notifier are from March and July 2015. Anyway, I'm happy to be rid of that thing; thanks so much!

I probably should've taken a closer look before removing the extension. No idea what it did; I guess I'd better change my passwords.