To add a bit more to the above answers, Johnny also feels abandonded by his mother. When Dallas finally comes to visit Johnny and Ponyboy at the abandoned church in Windrixvill, he brings a letter for Ponyboy from his brother Soda. Johnny asks if his parents have asked about him. Dallas tells him they haven't, and Johnny takes the answer pretty hard. Eventhough Johnny is neglected and abused at home, up to this point, he probably hadn't really accepted just how unwanted he was. But it's pretty hard to pretend your parents care even a little when they haven't even asked about you after you've been missing for a week.
It is only a day later that his mother comes to see him in the hospital; however, it has finally become very clear to Johnny who his "real" family is -the Greasers. Perhaps Johnny's refusal to see his mother is his own attempt to finally protect himself from her.
When Johnny is in the hospital, dying, his mother comes to see him. The nurse tells Johnny his mother is there and he says he does not want to talk to her.
The reason for this is made clear in the book. He hates the way his mother treats him. He tells the nurse that he believes his mother is just going to come in and tell him how much trouble he is causing for his family. Remember that Johnny gets beaten at home a lot, so he is likely not to feel much affection for his family.
Johnny's mother is such an unpleasant woman that Two-bit is near tears from thinking about how horrible it must be for Johnny to have to live with her. That's why Johnny doesn't want to see her.
I agree with the first editor, but I also believe that Johnny has been mentally broken down by his mother's words and hatred towards her son, that Johnny has nothing left to give emotionally. He does not want to see his mother because he also may believe that she has come to see him for only two reasons. His mother was told by the hospital that she had to come. His mother came to see him because she knows that he and Pony Boy have been called heroes and now that Johnny has done something to be praised for publicly, she wants to hang onto the kite tail of his temporary glory.
Johnny's mother may be feeling guilty and want some degree of self absolution from Johnny by actually making the effort to visit her son. However, Johnny is so mentally broken by her abuse, that he can not give that to her.