I have also have a hub with 3 buttons. Mine have all been setup and working great for well over a year. No changes that I am aware of with any of the setup.
Recently my Alexa routines cannot be invoked via the buttons.
The same buttons can control other devices eg Phillips hue but not Alexa. My hub has a wired connection to the network and the hub shows connected to the internet. The flic app on my phone shows the button presses.
I tried disabling and re-enabling the flic skill in the alexa app. I receive an email from amazon saying the skill is enabled but it doesn't work.
In desperation I deleted the buttons from alexa, disabled the alexa skill, removed the buttons from the hub, removed the hub from my app, deleted the app from my phone and went through the setup process again.
Now, I cannot get alexa to discover the buttons at all now. The buttons still work great for other actions.
All indications are that something is broken between the the flic and amazon cloud services.