+1 here. WP3.8.3, W3TC0.9.3, bluehost.com, PHP5.4,
Previously, without key-in CloudFlare API in W3TC, the speed & security remain function.
Recently, auto update to WP3.8.X, the CloudFlare start not function well.
If you installed WP-Control (cron job management), you will detected (need refresh to check) cron job cannot connect (host timeout & ansyc zone_setting) to CloudFlare network. (CloudFlare ticket submitted).
As above, I tried activate API in W3TC0.9.3 (conservative to upgrade to all major version upgrade). The problem remain unchanged.
Please kindly check your cron job event (schedule post, email schedule, minify clean up, page cache create & etc & others plugin cron job event).
Please note that I am also testing apply real cron job pratice in host server currently. (Normally, WP core cron job x000 miniseconds timeout issue)
Any solution will update here to share.