Problem

When a site-administrator invites a new user and receives the error message:

(warning) Something went wrong. We couldn't send your invitation. Try inviting that user again.

To replicate :

1. Log in to User Management as site-admin
2. Click on invite user
3. Add the new user email address in email addresses field
4. Check on JIRA software Application access
5. Proceed to click on "invite user":
   Refer to screenshot below:
   

1. You will see the error message below at the bottom left of the screen:

Resolution

It is best to check Product Access, for example for JIRA Software, see if the license usage has reached its maximum limit.

If yes, you can do one of the following to address this issue:
Option 1: Increase the license limit for JIRA software.
Option 2: Uncheck the JIRA software application access checkbox when inviting a user (in this case all newly invited users are not be able to use JIRA software features after invitation).