This past weekend, I performed a clean install of the Mac OS, which is 10.11.3 El Capitan. This seems to have resolved my backup issues. The root cause of all the problems I was having was with the Mac OS, NOT iDrive. I'm posting this in the event that it will help other Mac users who are having similar issues.
I would like to apologize to iDrive and it's technical support staff for wrongfully accusing them. I would also like to commend its technical support team for having the fortitude to try to resolve my issue even though iDrive was clearly not the cause. I remain a loyal iDrive user and would encourage other Mac users who may be having backup issues to thoroughly check their OS before jumping to conclusions, which may not be accurate. :)