Why would George never be able to make a Patronus after Fred's death?

George just wouldn't be able to recover completely from Fred's death. He would never again feel completely and utterly happy and at peace. The strength of the bond between them as twins was so great when Fred was alive that when he died George lost a part of himself. He wasn't ever whole again, as you would need to be while casting a Patronus.

My guess is that all of his happy memories include George, so they'd become sad in retrospect and wouldn't be strong enough to create a Patronus.

It is a bit strange that he'd never in future create new happy memories strong enough to work, though. Strange and depressing.

Basically what Flickerflame said. All his happiest memories include Fred, so when he thinks about his happiest memories, it makes him think of, well, Fred. And seeing as Fred is dead (most depressing rhyme ever), it would remind George of his death and make him depressed.