"[Your Site] doesn't support a secure connection with HTTPS" in chrome

Hi, I have 60+ websites. I've been using Flexible SSL for years but, within the last few months, I've suddenly started getting this message in chrome (but only sometimes) when accessing the sites.

Lately we've discovered that if you wait like 10 seconds, it may just kinda instantly load the actual page without touching anything.

Why is this happening and what can I do about it? Thanks!
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