A neglected Accutron watch will continue running, and keeping good time, for years after a mechanical watch would have ground to a halt.
As the oils dry up, and dirt and corrosive deposits from batteries and moisture accumulate, the gears turn harder. The tuning fork "motor" has lots of spare power though, and the circuitry compensates by drawing more power from the battery and it keeps the gears grinding away. It is a very common to find an Accutron movement with pivots (the tips of the tiny axles the gears run on) rusted solid in their jewels and twisted off. But even without rust, the pivots will grind away without oil. This cannot be fixed, and the parts must be replaced. A tiny bit of oil can preserve many expensive parts.
The only external sign of this increased friction and permanent harm being done to your watch is possible reduced battery life. But who keeps track of when a battery was last installed? Would you notice 13 months reducing to 9?
I recommend that Accutrons be serviced every 5 years. This will ensure that the pivots will always have oil, and will not get ground away. It also ensures that your watch gets routine inspection for water and battery damage, and has fresh gaskets to keep moisture out.
When I service your Accutron I will return it to you with a fresh battery, marked with the month and year I installed it, and "#1". I recommend you mark the next battery the same way, with the month and year and #2. If you have a jeweler install it, they should be happy to do this if asked. This way you can tell if your watch is running less than a year on a battery, a sure sign that it needs service. You can also know when about 5 years are up, when you pull out battery #5.