Remove your API keys from network-level and all sub-site settings, remove from https://theeventscalendar.com/license-keys/, re-enter the API keys only at the network-level, then re-try checking for updates.
If that still doesn’t work, manually update the plugins for now and hope it works next time.
A multisite license allows for unlimited sub-sites on a single multisite install.
Please let me know how this goes for you.