I used Totally Awesome to clean my awning two evenings ago. Had a few spots that it didn't remove. Picked up a bottle of Mold Armor. I've used this in the past for heavy spots. Works great.
edited to add that I also tried Magic Erasers with no luck.
So after using those two I have about 3 or 4 spots I just can't remove. The Mold Armor is stronger than Tilex with Bleach so I'm not sure what I can do to remove those spots. I've let the Totally Awesome and the Mold Armor sit for 30 minutes on the heavy spots and they mostly came out. Here are some pics of what I mean. The first picture is on the outside where the flap hangs down and on the roller. The last picture is just a full finished picture.