Yes, batteries do die.
Is the battery causing a focus problem?
The only way to know for sure is to try a new battery. (catch-22)
With a Panasonic camera here is something to think about.
A little over a year ago Panasonic changed the firmware in their cameras to where they can detect a true Panasonic battery. If the battery is not a Panasonic brand battery the camera will not let you use it.
If you have updated your camera firmware in the past year or so, it likely will have battery detection in it.
So be aware of what brand battery you are buying.
They did this because they were getting failed cameras where the battery had caught on fire.
The burned batteries were not made by Panasonic.
i.e. a cheap battery is not necessarily a safe battery.