I'll make a new answer for future reference But in the end, this didn't work for me.
It's not related to a single widget, it's all of them.
I haven't found a single one that updates at the moment.
I have several widgets that should update regularly: chats, weather, Google Fit, call logs etc; and none of them is updating.
As I already mentioned, I'm using a Motorola Nexus 6 with stock Android 6.0.1 on it.
I have all the latest version of the Android version for my phone, and have installed all security patches.
Including the July security patch from a couple of days ago. I don't have any special applications running that should customize my battery behaviour (like Greenify). Make sure you're not using Greenify or some other app to hibernate your apps. I have been trying different launchers, and have have noticed that the problem still occured.
If you hibernate those apps then they won't be able to update because they are not running in the background Clear the cache and the data for the widget apps in the settings and also for the launcher you're using. Then I got in the documentation of the widgets and found the problem.
When I reboot my phone, it updates the widgets one time, and that's that. For example, I have the widget for Google Fit on my home screen, and it is still showing the status from a couple of days ago; when I rebooted my phone.
I tried the Android N beta some time ago (I can't remember if the widgets updated then though). But I'm guessing the Android N beta has nothing to do with my problem? Are there some settings that I could have executed that froze my widgets?
But because there were some problems with applications I use daily, I reverted back to my old Android 6.0.1 build. Maybe something with battery optimizations or something?
I don't have to mention to you that widgets that aren't updating are very annoying.