It is a quartz watch, as others have noted. It would say "chronometer" on the dial if it was an automatic. The second hand will also jump from one second mark to the next and not sweep. The fact that you thought it had lost time after setting it the first time, but it hasn't since you reset it most likely means you set the time wrong the first time. I do this all the time -- set the watch to the wrong hour or ± 5 minutes off.
If the battery is going bad, there should be a change in the seconds hand behavior - it will start jumping by 2 seconds (maybe 3, I forget for this movement). If the seconds hand on your watch is making 1-sec ticks, the battery is fine.
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