I cannot fin any document here in AppleWorld or with Google [ screen record ios device ] OR [ screen record yosemite ] that indicates a limit of iOS > Yosemite screen recording, no matter what the end result.
I HAVE seen comments in the many How-Tos that inevitably pop up WebWide that they believe that this functionality was specifically developed and included in Yosemite for the very purpose of creating an App Preview.
Assuming the latter is correct, this would be considerably different than a continuous "shot" - Tap > Result, Tap > Result,Tap > Result, Tap > Result,
For this example - Tap > Result - it seems that 10 seconds would be more than adequate - and https://developer.apple.com/app-store/app-previews/ (an overview of App Preview) seems to indicate in the Getting Started section that this was intended to be used in conjunction with iMovie to edit ("stitch together") them into a 15-30 second finished product.
"Is there anything I can do to fix it?" When taking your experience and the researched outsider comments together, well... maybe not. Others may well have a better answer as mine is based on research
Have you posted this issue in the Developers Forum?