I have Faced the Same issue on my device. It was 2 years or so when I started experiencing the Problem. the Battery was draining inside 3 hours, even when the phone was in Stand By,flight mode .
When i checked my battery status
The battery Health was shown good.
I checked the Battery operating voltage during the same period and the discharge voltage using a Mulimeter. The was a bit higher than expected and operating range, meaning the Battery was short.
Under the circumstance, i changed my battery.
Inside 3 Months I experinced the same problem again. The issue was traced out to the Charger, which was sourcing by Battery with a Higher than expected voltage continously causing damage to the Battery.
1. Change the Battery, It would have already been short by now.
2. Check the Charger, (I dont know to check, i approched a specialist for this), get it replaced if necessary.
Now my phone is about 3 year old with still awesome battery performance. Only,issue at present is Touch Wiz RAM Hog, which wats up 80% of my RAM even on first Booth and Wiping Cache memory and disabling PreBuilt apps which I dont Use.