Wow that's bad. Not surprising, but bad.
My suggestion would be to possibly (If you're into doing this) replacing the whole front end. Take detail parts like the steering vains and whatnot, but the main forward rods would need to be made by hand, and of a sturdy plastic.
The good news is (I think) that the main body of the bike would be a similar rigid plastic to the rigid rods you would need to replace the flimsy ones. This means they'd weld together well with a good plastic welder like Devcon's or (My suggestion) Plasti-struct.
You'd have some cutting, fitting, gluing, and of course painting to do, but you'd have a bike that didn't droop.
Honestly, I'm planning to someday handmake my own speederbikes (For ROTJ) as the sculpt of the toy is way oversized, and I'd like to have a scale version.
Hopefully you'll be able to fix that bike of yours though. That's a shame that Hasbro's so cheap with their plastic, adn this is the result. Sheesh...