It looks like version 2.2004.22762.0 of the Cortana Beta app lost the ability to react on a wake word. Saying 'Hey Cortana' doesn't activate the app, instead showing a message that the key word is not currently available.
Saying 'Hey Cortana' makes the app show the following dialog:
The message says (in Italian) that the activation word is not available as of now, but will return in a future update.
It is not clear what causes this behavior. Quite possible that Microsoft is tweaking the speech recognition engine for Cortana, or makes some other changes to the app.
Cortana is a virtual assistant bundled with Windows 10. Cortana appears as a search box or an icon on the taskbar and comes with tight integration with the Search feature in Windows 10. Signing in to Cortana with your Microsoft account allows it to keep track of what interests you, save your favorite places to its Notebook, collect notifications from other devices, and sync your data between all your devices with Cortana enabled.
The Cortana - Beta app, when installed, replaces the current version of Cortana. Check out the app page on the Store here:
By placing Cortana in the Store, Microsoft will be able to update it more frequently. Also, this can potentially give the end user the ability to install Cortana like any other Store app.