Niether partying is acting to try to get the case in court for a final hearing or to file any motions and/or petitions.
If I understand what you are saying correctly, someone filed for modification of the SAPCR and they no longer wish to pursue the modification. If they do nothing, the petition for modification will eventually be dismissed for "want of prosecution"--a legal term meaning that no one did anything, so the court takes it off the active docket. Or the court will just let it sit there until someone sets it for a hearing or someone files another motion/petition in the case.
It can sit there quite a while. Some judges run rocket-dockets and move cases quickly. Others let them plod along. Either way, if you are the petitioner (and the other party did not file a counterpetition), you can file a notice of nonsuit along with an order granting nonsuit and the court will close the case. Or, if you were the respondent or there was a counterpetition filed, you can ask the court to dismiss the case for want of prosecution yourself.