Tilex is nothing but packaged bleach + detergent, so probably won't do any more than what he has already tried. Spray and roll-up with Oxiclean is another alternative, but again is just detergent + bleach.
I would make one more try using a strong bleach solution with a heavy duty detergent, e.g. Simple Green or similar. Laundry products like Oxyclean aren't all that strong and the awing is tough stuff. If it's a vinyl awning, nothing short of battery acid is going to damage it. If woven acrylic fabric, you may have to apply new waterproofing after. Be careful of your eyes when spraying strong bleach overhead. And wear an old hat and old clothing, cause it's gonna get bleached!
If that doesn't work, I would say that you have tried everything that can be done and the next step is to replace the fabric. Not really all that hard, or even terribly expensive.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL