Did you need to use a countersink at all moving to a larger screw?
I did not. I used pan head SS screws readily available at box stores.
Saurd, I just realized from your photo that your awning rail is not incorporated into the rain gutter like mine is. I'm on the fence which I'd prefer. I like the rain gutter attachment on ours because it doesn't leave a collection point for water and leaves and such on top of the awning barrel but in the same breath, the 19' awning on ours is pulling a lot of force on the rain gutter that is the "cap" on the roof edge termination and any failure at this location almost immediately introduces a leak where water is channeled to.
You could try larger screws where your factory ones are pulling out and take care hand tightening them so as not to strip them, maybe even dap a bit of sealant/adhesive in the hole or dip the screw prior to installation to help seal it and limit vibration back out. You could also use 3m 5200 as a last resort if it keeps happening. I have a tube of it I was going to use on the rain gutter rail if I kept chasing my tail with screws backing out. It is serious, PERMANENT stuff.