First check the new battery with a voltmeter.
Not all "new" batteries are good.
Good deals on button batteries to be had on eBay, stick to branded batteries.
I had issues with an 04 focus. The new battery lasted only a few days, so I washed the fob in isopropyl alcohol (IPA)( Do this at your own risk!!), left to dry and reinserted a new battery. The remote has now worked for over 12 months.
Bob