To prevent the Hub from getting a new IP again, you can go in your router and set a fixed IP in the DHCP settings for it.
The hub getting a new IP should not impact Alexa at all. Since it is cloud based, it does not use your internal LAN IP at all. Check the logs for errors.
DO NOT delete or otherwise change anything in the Alexa app on the hub. You can however open that app up and click Done. Then check logs again for any errors.
Check if hub is connected to Hubitat cloud system
- Go to: My Hubitat > Registered Hub
- Click the details button for your hub.
- Is the Last Checkin recent?
Another way to verify if hub is able to connect to internet
- On the hub UI, go to settings > Network Setup > Network Test
- In the ping test, type in cloud.hubitat.com
- Post screenshot of results.
You can also go to the Alexa skill (from the Alexa mobile app), disable it, then enable it again. It will have you log into your account again and select a hub. This should retain all your devices you already have shared and just reconnect the two system together again.