Once you open a jar of jalapenos the opened jar of jalapenos will last up to 2 months as long as you keep the jar of jalapenos in the refrigerator.
Jars of jalapenos can stay out in the pantry or on the counter as long as they're not opened but if you open the jar of jalapenos you have to keep them refrigerated to make them last.
As long as you keep the jalapenos refrigerated it will last in the jar for up to 2 months before going bad.
When the jarred jalapenos go bad they'll have a bad smell to them and or have mold growing on them which they should be thrown out.