Many times I am asked if the accuser can just "drop" the charges against the defendant. Unfortunately, that isn't as easy as it is on television.
In a criminal case, the charges do not belong to the victim, so the victim can't "drop" the charges any more than the victim could increase the charges. Criminal charges are brought by a District Attorney or Solicitor on behalf of the victim, who is just a witness in the case like anyone else. Victims can communicate with the prosecutor to express their disinterest in seeing the case prosecuted, but the ultimate decision is up to the prosecutor.
In most cases, the victims made statements to the police, either written or oral, when the case began. The victim may have been the one who called the police to begin with. If victims later make statements contradictory to their original statements, they can be charged with filing a false police report or the felony charge of giving false statements.
There is a big difference between saying "It didn't happen" and saying "It happened, but I no longer care." If the victim says that it didn't happen, then the victim is likely admitting that they lied to police originally and now the victim can be charged. If the victim says that it happened but they don't care anymore, they are just reinforcing their original statement that it happened, which strengthens the prosecutor's case.
All the prosecutor really cares about is whether it happened. The fact that the victim may now want to drop charges doesn't mean the prosecutor will drop charges.
A twist on this issue was when I was told by a client that the "victim" is offering to "drop charges" in exchange for money. He asked me if he should pay it. That is a horrible idea for both parties.
By offering to refuse to cooperate as a witness in a criminal case in exchange for money from the victim was asking him to join her in the crime of witness tampering:
"A person who is or may be a witness at a trial, hearing, or other proceeding before any court or any officer authorized by the law to hear evidence or take testimony and who receives or agrees or offers to receive any benefit, reward, or consideration to which he is not entitled, pursuant to an agreement or understanding that his testimony will be influenced thereby or that he will absent himself from the trial, hearing, or other proceeding, shall, upon conviction thereof, be punished by imprisonment for not less than one nor more than five years."
----GA. Code 16-10-92 Witness tampering - witness perspective (Georgia Code (2012 Edition)
In these situations, call the victim's bluff. Keep good records of every email, text and voicemail where they offer to "drop charges" for money. Do not agree. Just let them keep offering.