Something changed with respect to the networking layer EpicTable relies on--either due to a Windows update or a change at my hosting provider. I have a new version that changes the interaction with the invitation service to adapt to this. You can download 1.3.7 at http://www.epictable.net/downloads/EpicTable/1/latest/GA/0
Check it out. It should solve your invitation problem.
Sorry for the disruption of service, and thank you to the people who reported it so I could get this fixed.
While I was releasing a new version, I picked up a one-line change that solves an issue with the background of one of the panels not changing when you change themes.