Answer: Container plants can be a challenge. Peppers (and other plants) can wilt due to either over or underwatering. Although peppers prefer a soil that is evenly moist, it should not be sopping wet. It is possible that the soil mix is either not draining well or is draining too well, or that the plant did not root out into the soil in the pot but instead the roots stayed in their original little root ball. You might gently check and see if any of these seem to be happening.
Another possibility, if it is in a windy spot or in a spot with reflected heat, or if the pot is rather small, is that it is simply drying out very quickly and you need to adjust the conditions or water more often. Terra cotta can allow soil to dry faster than a plastic pot would because the sides are porous and allow the moisture to evaporate.
Finally, it may have reached its mature size, or the fruit production is taking so much of its energy that it is not growing. Container plants do need to be fertilized on a regular basis with a water soluble fertilizer according to the label instructions. You might also top dress the pepper with some compost every few weeks.
I hope this helps you trouble shoot the problem.
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