I doubt very much that you'd get bee's on a 4th floor windy balcony, just MHO

Bees are necessary, but not for pepper pollination *smile*. There's a few things that can cause flower drop, but my guess is your S. Florida sun/heat.

Chiles are self-pollinating.

Thanks everyone! Since my last post I have replanted it into a large pot and added a stick to sturdy it. I’ve since lost about 3 more flowers.

As far as balcony height goes ... I do get bees on my 3rd floor balcony.

You don't need bees. I grow my peppers in a glazed porch. No bees in there. As for the flowers dropping. Is it just the white part or the whole flower including the green bulbous back of the flower? If it is only the white you may well still get peppers. The first time I grew them I was surprised there was no baby fruit like on tomatoes. But they developed in due course.

Flower drop probable causes:

1. Day temp too high >95F

2. Night temp too low <65F or too high >85F

3. Too much nitrogen fertilizer

4. Too much water

5. Low light levels (reduces fertility).

6. Very low humidity (reduces fertility)

7. Poor air circulation (air circulation contributes to pollination).

8. Lack of pollinating insects.

9. Size of pot

10. Too much mineral in feedwater.

11. Too much grower attention/anxiety.

I might suggest extra phosphorus. It helps plants have strong flowers. The problem is probably temperature or soil-related. As others have alluded to, peppers have perfect flowers (which means they have both male and female parts in the same flower). Wind can actually cause them to pollinate themselves. However, I'm not sure if peppers like lots of wind. If the stems and branches are weak, you may need extra potassium (which can help with heat-tolerance, too).

Your plants look fine, but in my opinion, based on the picture, you probably need an even bigger pot for a plant that tall. Some tall peppers do fine in smaller containers, but many don't like it as much. However, Florida's a very different place than where I live (and I know I've seen pictures of very healthy pepper plants loaded with fruit, in tiny containers, coming from the southeast). I don't know if it's the humidity, their choice of soil, their fertilizer, or what.

You should also realize that even in a garden chalk full of bees, they tend to prefer many other kinds of flowers over those in the Solanaceae family. I see small bumble bees and flies similar to hover flies on them more than honey bees.

@Alexis, what kind of peppers? I'm just noticing that they look like some baccatum I'm growing.