they'll live until you or the weather kills them. there might be a size limit, but unless your name is jack frost, it's hard to kill a pepper.

Someone once told me that peppers can live up to 15 years, but 7-9 is about average.

They will live a long time, but, I've heard that at some point production decreases...

I had a couple lemon drop plants for 4 or 5 years and never noticed a slowdown. But, I also pruned them back for overwintering indoors every year. So, they had to grow new foliage and roots each year. Not sure if that helps keep them vigorous or not, though. I just know I had no issues in that amount of time.

Thanks I decided to let them grow another year and plant some new ones along with them.

Jalapeno should be quite easy to start from seed in Texas.
Just grow one more from seed, as back up.