How cold is it there right now (day and night) and have you been feeding it? How much Sun is it getting?

Well I live in Houston Tx so during the day here it's mid 70's low 80's and at night it's mid to high 60's. I am feeding ever 14 days and on sunny days it's getting 4-5 hours of direct sunlight, and on average it gets 3 hours a day.

It is a very leggy plant so clearly isn't getting enough sun. But blossom drop is a condition that is primarily caused by air temps and inconsistent soil moisture levels. When growing in containers it can be especially difficult to stabilize the soil moisture levels - especially when the container is too small.
Blossom Drop FAQ

I see it also appears to be dropping leaves and that is a clear sign of over-watering or poorly draining soil Peppers need to dry out between waterings. So what mix is in the container? How much and how often do you water? What have you fed it and how often? What size is the container? Where are you located and what have the average air temps and humidity been? And you must do something to get it at least 2-3x the sun exposure it is getting.



Dave

Yup, needs MORE sun!

In addition to the advice above, I'd recommend helping the (self) pollination. Pepper (and tomato) flowers contain both male and female reproductive parts. The pollen falls from one part to the other. But sometimes it doesn't, and the flower just dries up and falls off. It is well known that shaking the flower helps that fertilization happen. Usually wind is enough to do that shaking. Such flowers pollinate poorly if there is no wind, or if they are well sheltered from breezes. In fact, that's why pollination needs a specific temperature range. If it gets too hot, the pollen tends to get sticky, and is reluctant to fall. But your air temps sound fine. A good trick is to give the flowers a flick or tap with your finger to help that pollen to fall.

I have jalapeno peppers that get 4-5 hours of direct sunlight on sunny days, and they produce admirably. But yours does look a bit leggy. Are those sun hours of yours when the sun is up high? A few hours of direct but low sun isn't worth much.

I live in an apartment complex so its when the sun is in the western part of the sky I will have to try either moving the plants to by the front door so they get better sunlight or try and find another way to get them to produce. It is humid here right now so I'm affraid that might be having an issue with them growing properly.