I agree with what Arthur Rankin (Rudolph's producer) said. He said she was abandoned by a little girl and suffered depression from being unloved. But there's more that the Rudolph adds to Dolly's plight. Charley-In-The-Box says that a Misfit toy is one that
NO little girl or boy loves. Dolly was likely rejected by every child, and the one who abandoned her was the last draw . . . the one that made her depressed (a.k.a. "noone loves me").
I don't think "crying" was the reason. Hermey the Elf's boss even says "we have dolls that cry, talk, walk, blink, etc . . .", which must have been the type of things that little girls wanted dolls to do. Dolly could do all these things, given the fact that she is shown to be a unique rag doll . . . being alive and sentinent.
There's been many other valid theories I've heard (behind the official psychological one) that could be at play . . . which might have led to Dolly's depression. People have said, "She has no nose", "Her dress is Tacky", "She says HOW DO YOU DO instead of MAMA", "She's a rag-doll instead of a real-looking doll" and many others. I personally believe that these and others might have been the relative "reasons" that each little girl had for not wanting Dolly . . . all leading to Dolly being on the receiving end of CONSTANT rejection. Dolly's depression then was borne out of feeling "I'm not good enough for any little girl" and "I'll never be wanted", no matter what she did or didn't do. The final abandonment from the little girl that Arthur Rankin mentions kind of cruelly "summed up" these notions in Dolly's mind and made her "give up" on ever being loved . . . UNTIL RUDOLPH AND SANTA FINALLY COME THAT FOGGY CHRISTMAS EVE at the end of the Rudolph story, and find her a happy home.