Is My Kirium Battery Dying?

I have a Tag Kirium bought in 2001. I've only rarely worn the watch and it's still in showcase condition. I replaced the battery about three years ago. While wearing the watch today I noticed the stopwatch second hand is stuck in the 35-second position. The stopwatch doesn't appear to be working either. The watch is keeping proper time. Is this an indication that the battery is going? The watch has never been dropped or banged and when the battery was last replaced the Tag authorized repair service said it was clean and in perfect shape. Anyone have an idea what's doing this? Thanks much.