We do a lot of battery changes, and there are some things to keep in mind about quartz watches and batteries in general.
If you change the battery yourself, do NOT touch the battery with your fingers, use finger cots. Likewise, do not touch the watch movement itself or use a vise (or a hammer) to shut the snap back case. That last one is common sense, right?
Anyway, we do see fairly regularly a lot of fresh batteries in watches that do not run, or fail soon after battery change, now why would this be, you ask?
Quartz watches are fragile, in some ways more so than mechanical watches. They are very susceptible to magnetic fields and radiation, and a strong magnet will kill a quartz dead. So you want to keep your quartz watch, or ANY watch, for that matter, away from cell radiation or other types of electromagnetic radiation and magnetic fields, ESPECIALLY cell phones.
Quartz watches have a relatively short life, a cheap one maybe a year or two, the more expensive ones may last decades, but that's about it. Mechanical watches will last much longer. The average age of the ones in our showcase is 60-70 years old. The oldest one we ever repaired was well over 200 years old, and is still running today.
Quartz watches, if left to die and thrown in a drawer, will tend to get sticky. The gear train may become stuck as the microscopic amounts of lube dry out and the plastic components degrade. The battery might also leak and make a real mess.
Putting a new battery in a watch that hasn't run in many years may result in a detectable pulse, but the hands don't move. It looks like the watch isn't running, but it is.
The quartz movement generates a weak impulse, and any friction or stickiness at all will mean that the circuit registers an impulse, but the rotor won't move, or the second hand won't move, maybe the entire motion works is too sticky to move. We have a machine that 'pushes' the gear train and makes the watch pulse rapidly, spinning the hands at a high rate. This sometimes unsticks the watch, and it will work normally.
Sometimes the watch is too gummed up. You can clean it out, but it is cheaper to replace the quartz movement, and a better idea too, because the new movement is fresh and has a warranty. Circuits fail, parts wear out, coils get touched.. There is a switch in the stem, so that when you pull it out, it stops the watch. It doesn't actually stop all electrical activity, but diminishes the draw so the battery isn't being subject to a full load. The switch eventually wears out, and the watch will stop and start intermittently.
This is actually quite common. Even a brand new Quartz watch, if left in a drawer for a couple years, will degrade markedly. Off-gassing of the plastic components will fog the inside of the crystal and degrade the parts and electronic contacts and wires. Swiss quartzes generally are better built, (They often have jewels) and will last longer, but they still fail much sooner than their mechanical counterparts.
The footprint of Quartz watches is much larger than mechanical ones, and the recycling that must accompany them also contributes to environmental impact. At the end of a typical year, we have 5-10 pounds of button cells to recycle, and many more pounds of discarded cheap watches that cannot be recycled.
I'm all about history and micro-mechanical engineering, so I love mechanical watches, which are still manufactured in large numbers and have a much smaller footprint to boot.
Keeping your quartz watch running with fresh batteries and warm on your wrist will make it last longer than if it is neglected, kind of like if you parked your car for a couple years and didn't run it.