Same thing is happening on the footer on my site. The most recent post displayed in the Instagram block is from 4 months ago... I just now caught the issue.
If you log into your Square Space account and go to Settings/Connected Accounts, you should see the connected social media accounts you have already connected. Chances are they have expired. Click on the red notification that says "Unauthorized - Remove or reauthenticate this account for continued usage." Click on the site in question and it will allow you reuthenticate it.
Should look something like this:
Your Social Media Name Here
Pull Enabled
Unauthorized — Remove or reauthenticate this account for continued usage.