Garden help?

I just uploaded 3 photos of my Cherry Pepper plant in the hopes that someone out there in the internet land, can offer me help of advice.
(Note: The same exact thing happened to my tomato plant last summer!)

I live on the second floor apartment and I have a small balcony. It gets full sun from the morning sunrise until about 11:30 or so. I have the plant(s) in plastic pots about 8-10inch diameter.
As you can see from the photos here. The plant appears to be very healthy. Leaves are nice and green, etc. I've got LOTS of buds. BUT... the buds eventually burst open into the flowers which also appear to be healthy. Then after a day or so, the flower starts to wither. Eventually, the flower drops off of the plant at the point where the stem of the flower joins the main stem (approx half inch from the base of the flower).
As I said, this same behavior also happened last summer to a tomato plant that I had, and although I had lots of flowers, and what I though was a nice healthy plant, I did not get ONE tomato at all. It appears to be happening again with my Cherry pepper plant too!
( I did try pollinating the flowers too on the tomato plant with a brush, to no avail).

I'm posting this in the hopes that someone with a little more gardening knowledge than I can offer some advice. As of this Saturday though, I plan on donating this plant to my mom's garden in the hopes that in a new environment where the plant will get full sun all day long, perhaps I can get ONE red hot cherry pepper out of this thing.

For what it's worth, both the tomato plant and this cherry pepper plant are ones that I started from seed from the previous year.

Any advice would be appreciated. I'd like to have a small garden on my balcony, but so far the only thing I can seem to grow successfully is basil.