Answer: Unfortunately, I am not certain if you have a pepper plant (the vegetable pepper) or if you have one of several woody plants commonly called a "pepper tree." But, in general dropping leaves could indicate a pest or disease problem or under or overwatering.
Watering is a fairly common problem with container and with garden plants. The soil should be kept slightly moist like a wrung out sponge, not sopping wet and not dried out. With container plants, there should be a working drainage hole in the bottom of the pot to allow excess water to escape. If there is a saucer under the pot, empty it after watering the plant. How often to water will depend on the weather, the size of the pot in relation to the plant, and on the soil mix. Use your finger to dig into the soil and check it. If it is still damp, do not water yet. Do not wait so long between waterings that your plant wilts. When you water, make sure it is soaking into the soil and not running out between the soil and side of the container.
In the garden, you may need to water occasionally to supplement rain. Again, use your finger to check the soil. If it is still damp, do not water yet. When you do water, water slowly and deeply so it soaks down to the deeper roots. Apply it slowly at the soil surface and avoid wetting the foliage. It is better to water less often but deeply than to sprinkle lightly every day. After watering, wait a few hours and then dig down to see how far the water soaked in; sometimes it can be surprising.
If you do not think watering is the problem, I would suggest you consult with your local Cornell extension and see if they can help you diagnose the problem and suggest what to do for your plant. I'm sorry I can't be more specific long distance.
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