how much and how often do you feed it? could be nute burn, could be calcium deficient and or nitrogen and magnesium deficient. check this link out...its great for helping you to understand what the 16 nutes are necessary for plant growth and what each nutes role is, as well as a great description of what each deficiency will look like. hope it helps and good luck! http://www.ncagr.gov/agronomi/pdffiles/essnutr.pdf
I had a couple that where burnt I flushed rhem then repotted and both rallied hard! They were beautiful again in a couple of weeks. Good Luck let us know how it turns out.
I had been fertilizing mine every two weeks and ended up burning them. Apparently peppers are extremely hardy and need very little attention. It makes me sad that my babies don't need me and think I tried to kill them.