This is a nice little time, I just think it needs more difficulty scaling. Making the camera scroll faster, more frequent obstacles, more types of obstacles as you climb. It just seemed too easy to keep the run going. The sprites and sounds were simple but effective. I liked the presentation plenty, I just think the game needs more going on if you want to have an endless experience like this.
Maybe a rockslide that takes up an entire side of the screen for a few seconds? Something to pressure the player to stick to one wall and spend a bunch of stamina.
Also, a check so that birds can't spawn right where you're hanging would be a nice addition!
Still, as I said, what's here is very good!