Sorry to hear about the trouble caused.
With Sign services, there was some outage reported. Which has now been rectified, and services are back. Please check at your end; there is likely a chance that your Adobe Sign service might have been impacted due to that. But it should not be up and running fine.
If not, then login to Document Cloud web and see if you can access the sign service.
If it's not affected because of that, then try this:
1- Restart Acrobat
2- Run this cleaner tool to remove the existing installer and application’s file traces:
Download the Acrobat installer from here:
Nothing works?? Please share the screenshot of how does Specify where the recipient must sign button looks like at your end.