If the solution needs to be specifically CBS This Morning available specifically through CBS All Access, you probably need to call CBS All Access Customer service at 888-274-5343
It is silly to only provide paying customers just the clips of This Morning considering that clips are already made available for free online.
If you are only paying for CBS All Access for This Morning but not getting it, switching to YouTube TV or Playstation Vue might be the best way to accomplish that. Both seem to carry CBS broadcast TV and have a DVR feature.
If you are willing to accept alternatives to This Morning, then I would suggest trying Newsy which doesn't require paying an additional fee and I feel provides better quality in reporting. CBS corporate has shown they are willing to heavily dictate editorial control which I feel undermines journalist integrity. CBS is a $20+ billion company and have their hands in a lot of things were corporate has a clear conflict of interest when it come time to decide what news gets reported and what it's down played when reported. While I am willing to provide suggestions above that try to stay true to your initial request to watch CBS This Morning outside of when it plays live, I also really need to ask if the quality of the program is worth jumping through hoops for.
If Newsy isn't to your liking, there are plenty of other news sources on Roku we can suggest.