In some cases, the SquareSpace "Ajax Style" Templates do not completely refresh iframed content when navigating within the website's primary navigation links.  We hope this issue will be resolved in the near term, but until then there's a workaround solution.

Step 1: Start by adding a new "NOT LINKED" PAGE where you will embed your calendar.  Name the page and navigate to this new blank page.  This is going to be your new calendar page.  

Step 2: Embed your calendar into this new "NOT LINKED" page.  Add content and use the Embed Block.  Be sure click the </> and then paste your calendar code.  Click OK > Apply > Save

Step 3: Copy the Complete link for this web page that contains your embedded calendar. This link will include https://www.yourdomain.com/eventcalendar or something similar. If you go to the page's SEO settings tab, you can copy it from there.
 

Step 4: Under the "Primary Navigation" area click the + and under the "Other" section add a "Link" with the chain icon.  This will allow you to paste the complete URL to your new page and this will load your iframed calendar page correctly.

Step 5: Paste your complete calendar web page URL into the link field that appears. Save.

Step 6: Go to your website while not logged in.  You should now be able to navigate to your web page that contains your iframed calendar and have it load properly.