I cloned the site (can’t afford for it to be down) and updated WordPress to 4.2.1, disabled all the plugins except the basic EC. When ECPro was activated, the message “Your version of The Events Calendar is not up-to-date with one of your The Events Calendar add-ons. Please update now.” Again, if I click ‘Please Update Now’, I get:
The plugin is at the latest version. If I deactivate ECPro, the message disappears. Seems to have been related to the version of EC that was installed.
I then re-installed EC (v.3.9.3) reactivated at it worked. So far everything seems ok.