I'm having this issue for the first time. On a fresh install of WP, with some plugins and a premium theme, TablePress is not showing up in the admin menu and I can't access the plugin page directly "You do not have sufficient permissions to access this admin page."
I tried to reinstall the plugin, deactivate the others, switch back to TwentyFourteen, nothing works. When I look at capabilities in User Role Editor, the tablepress' capabilities are not even displayed. I don't have this issue on other site with the same plugins setup.
The theme in place is using the "Cherry Framework", but it doesn't seem to be the culprit since I have the same issue using TwentyFourteen.
I can provide you access to the admin to help debug this.
On a side note, I don't have this issue on a local install with the same setup, TablePress is displaying alright.