This question is an exact duplicate of:
When I changed my avatar on Physics a few days ago, it briefly displayed at the top, then after a few minutes disappeared from the toolbar.
Later it disappeared from my questions and profile as well. Further inspection revealed that it was hidden behind an HTTP 403 forbidden result with a CAPTCHA, courtesy CloudFlare. Answering the CAPTCHA restores functionality, for now.
This is the same problem as CAPTCHAs are intermittently blocking CDN content. Randomly knocking out resources is unacceptable for a CDN. Please address this.