My awning is vinyl, and stays wet a good portion of the year due to the rains here in FL. Consequently, it had mold growing on it.
In the past, I had washed it with a soap and bleach mix, using an RV brush. Kept everything wet for 10 minutes, then rinsed off. Worked pretty good.
A couple of weeks ago I found a YouTube video where a person sprayed his awning, rolled it up, and let it set for 20 minutes or so.
I bought a $10 pump sprayer from Home Depot, and made up a couple of gallons of water with a good dose of bleach added. This made applying the mix much easier than using an RV brush.
After the 20 minute soak, I rolled the awning out, and rinsed it off. While it is almost 9 years old, it cleaned up REALLY well.
So if you don't have great success with your current method, try rolling up the awning wet with the bleach solution and allowing it to do its magic.