Why doesn't Time Machine do scheduled backups after my Yosemite -> El Capitan upgrade?
I'm having a very similar problem after upgrading to El Capitan, except that I can not repair the disk, my attempt always gives me a repair failed error.  I don't have an answer, but I think I can verify that the issue probably isn't related to any third-party extensions as I'm operating without.  So at least I may be able to help rule out those as a source of the problem.