Try running the URL (of the task) in a CFHTTP call, and dump the cfhttp variable after that, to see what happens.
And you ARE confirming that it’s an https url? You probably WILL find that it’s about an issue of the JVM underlying CF having an issue with the SSL/TLS support of the server being called (in the URL). It MAY be that you need a certificate added to CF (to the JVM underlying CF), if the site you’re calling has something requiring you to have a client cert in CF.
But more typically it’s just that the TLS/SSL support in the server being called has changed and is now of a level which the underlying CF JVM can’t support. In such cases, the solution nearly always is just a need to update the JVM CF is using, especially to Java 8. You mention being on CF10. The JVM CF originally came with was Java 6 (1.6). Later installers (in 2013) updated it to Java 7. And CF10’s update 14 also allowed you to update to Java 8. More at https://coldfusion.adobe.com/2014/10/coldfusion-10-and-11-support-with-java-8/.
And if you try to update the JVM and have trouble, consider the many possible problems and solutions that I outline in a blog post here:
http://www.carehart.org/blog/client/index.cfm/2014/12/11/help_I_updated_CFs_JVM_and_it_wont_start
/charlie