Yes, your attorney can request to be relieved from representing you if you fail to sign a substitution of attorney form. The grounds are typically not stated by the attorney, since to do so is typically a violation of confidences, but the usual reasons lawyers get out of cases is because they aren't getting paid or because some kind of conflict has arisen between the attorney and the client. As a practical matter, if the lawyer wants out, they're going to be allowed out. You need to talk to your lawyer to find out what the problem is and see if it can be fixed.
You do not state why your attorney wants you to sign a substitution of attorney form. It is possible that the letter you wrote to her was the impetus for her request to withdraw from your case? Or maybe there are other reasons? Have you paid your bill for her services? Have you responded to her inquiries and been truthful with her? Those are some reasons why an attorney may want to get out of a case.
In any event, if an attorney is requesting to be substituted out of the case, it generally means that the attorney-client relationship has deteriorated for some reason. Going to court only makes it worse as it takes time away from the attorney's practice to have to attend a court hearing on this. I would talk to her about it and if the situation cannot be resolved, I would sign the document she is requesting and seek other counsel.
Good luck to you,