That is rather odd. It might be a problem with the DDOS protection. The handshake is not working properly; but the certificate stays until it tries to access your site. I am receiving an Error 525 SSL handshake failed.
I would try to temporarily disable the DDOS protection; to see if that is the problem. Otherwise, it is a problem with the certificate being issued by the authority.
It will take the Admin or an InfinityFree staff to look into it further. In the meantime, you can make a backup and try uploading a basic index.html or index.php file. To see if it completes the handshake or not.
If you head to the Cloudflare Control Panel, under Crypto/SSL you will see different SSL modes, these include None, Flexible, Full or Full (strict). Full & Full (strict) will not work with the free hosting platform. Switch the setting the flexible and the issue will resolve itself. @h4xr0x