Sliding Patio Doors weather stripping between the doors

I'm afraid I cannot determine a replacement for you based on these photos. In order to help, I will need you to remove an undamaged sample and show me a clear picture of the end profile. The video below will clarify what I mean.

Thanks for clarifying. Unfortunately, without the original seal to use as a reference, there isn't really anything that I can recommend with confidence. I don't know anything about your door, who made it, the size of the gap you need to fill, or even how the old weatherseal was meant to install. 

It does look like your door is wood; if so, you could consider something like the 58-169. This has a nail on flange, allowing you to adjust it to the best position possible before nailing it to the door. However please understand that this is an educated guess and that I cannot guarantee it will work for you.