Hi there, Eddie–welcome to the forums!
Sorry for the trouble here. I see what you mean. Normally, the next month link would hide if there were no upcoming events in the future months, but it appears you do have upcoming events in this months.
I tried to replicate the issue on my own setup and came up short. Do you notice a difference when you activate a default WordPress theme (like Twenty Fifteen)? How about when you deactivate all other plugins, except for The Events Calendar and The Events Calendar PRO? Finally, how about when doing both of those at the same time?
These steps are outlined in greater detail here.
Let’s start there and see what we find. 🙂
Cheers!
Geoff