I had a stable working CF11 environment running on Server 2008R2, with several Scheduled Tasks running using https urls. As far as I know, nothing has changed, except the SSL certificate for the domain seems to have been renewed.
If I manually run the tasks via the CF Admin, the message says the task ran successfully - it didn't. I have them set to log the result, and the text file says Connection Failure. I even tried to run the same https URLs from another CF server, nope. I can execute the https URLs from a browser successfully.
I have followed the instructions for adding the new cert to the keystore. I actually did it via CertMan (a really cool CF plugin for CFAdministrator which lists all the stored SSL certs and enables you to install others), and via the keystore command prompt. Still doesn't work.