The message I got back from Time.ly support regarding this issue reads:
You can try our newest web app Journey calendar where we have done tremendous enhancement on the overall functionalities and interface.
We can also assist you to transfer your current events as soon as your Journey calendar is activated. The Journey web app is an embeddable calendar which does not require to download any plugins, you can easily Sign up, pick a plan and embed the calendar on your website. You will get free 30-day trial with any of the available Plans. If you need help with setting up your Journey calendar, please feel free to let us know.
So, looks like they’re not going to bother to fix the problem. I’ll be searching for a different plugin…