The website exists already at https://persist.tv. Don't worry about the existing placeholder logo there. I'm not particularly attached to it.
To give you a better idea of what this is about, I've included a screenshot of the app in action. On the left is my Krav Maga instructor demonstrating a technique and on the right is me following along. I get to watch that back, rate myself and try again or continue.
Although the site was initially designed for martial-arts/self-defense type stuff, I don't want that to be the sole focus.
I want an icon that I can use as a favicon and for listing in app stores (ie simple and square). That may be part of the logo or a separate character.
Ideally the logo should communicate achievement through persistence and (if possible) television/broadcast.
Some keywords that may help:
Sweat, effort, achievement, connectivity, mirror, side-by-side, learning.