Check your email servers logs for the failed email address, that should provide you with the cause. Possibly your Mail server is being rejected in an RBL for Spam like behaviour or similar. Without more details of your MTA and logs of the same it is going to be a needle in a haystack to find...
Change the <img src="http:// part to https:// for the avatars in your template or backend panel. It is loading mixed-content over https and http so https gets broken! thats why.