Lots of questions:
Is there drainage in the pots - specifically, are there holes in the bottoms? Did you use potting soil, or "dirt"? How often do you water, and how much water do you apply at one time? Are the plants in full sun?

The hose nozzle we can see in one of the photos makes me wonder if you're really saturating the soil, or just sprinkling it. Ideally, you'd water until there was steady runoff from the bottom of the pot, and then not water again until the top inch of soil felt dry to the touch. If the soil was ever too dry, you'd want to sit the whole pot in a tray of water until the soil was saturated, since really dry soil may shrink and have trouble absorbing water. If there are no drainage holes, none of this would work, obviously.

And, if I were growing arbs in pots, the pots would be at least twice as big as yours in relation to the size of the plants. Not that it can't be done with smaller pots, it just takes more steady care.

There are drainage holes in the pots, I drilled them myself. Maybe I drilled too many holes? The pots are about 4 feet tall and the diameter is about 1.5 feet. I filled it with a couple pieces of rocks and broken pieces of bricks(not alot) to add weight to prevent falling over and then styrofoam nuts to about half height of the pot. The rest I used garden soil I bought from Homedepot. Maybe the water is leaking too fast? Should I just take out all the rocks, styrofoam and fill with soil?

Some plants are in full sun, some are not. The ones are not in full sun are slowly drying and dying. I am water 1-2 times a week, until water rises up about 1-2 inches from the top soil. Basically, I think water a lot when I do water them.

Growing shrubs in a pot can be challenging! While those are handsome pots, I can see several problems you will have. The narrow base will make them more prone to tipping over when there is wind with the arborvitae on top. You have a quite restricted amount of room for roots, width-wise, and since the bottom part of the pot is filled with rocks and styrofoam, there isn't much root depth. The less soil and the narrow pot means that temperature and moisture will fluctuate more than with a bigger pot.

If I were you, I might try getting a wider (& as deep as possible) pot and filling it with potting soil, not garden soil, and replant your surviving arborvitaes. Garden soil tends to be more dense than potting soil, and without enough air spaces, the plants' roots don't get enough air. (In the garden, soil gets aerated by worms, moles, etc as well as having organic matter constantly added from on top naturally.) Also, potting soil is lighter in weight than garden soil if your situation has weight limits. Water deeply when the soil feels dry when you stick in your finger to the first knuckle. Since some of your plants get more sun than others, you will have to check each plant separately. Too much water for your shady plants may be what killed them. Also, in general, arborvitae are sun plants, so will want at least 6 hours of sun to grow really well and full, though they will grow with less, just not as densely. They won't be happy in full or almost full shade.

I am assuming that you are planting to block the view beyond your railing or to give some privacy. If you decide your conditions aren't good for arborvitae, some other plants that are tall enough and full enough to help give you a green wall and are tolerant of living in pots include ornamental grasses (there are some quite full, tall grasses, though they will need sun), bamboo, and vines on an obelisk or trellis (some clematis will tolerate part shade, and there are many annual vines, though most of those like sun.) I've also heard of folks fastening bamboo screening to a fence, which lets in some air, but provides some privacy, and then planting in front of it. Since the plants don't need to be quite as dense to ensure privacy, you will have more choices.

There are container and balcony garden forums here on Garden Web where you may get more info. Read their FAQ's (if they have a set) and search for arborvitae and evergreen. See what info you can get just from reading a bunch of posts, and then ask for information that you still need. You can also find books and magazines in your local bookstore or library that will have photos to inspire you with a variety of choices. Researching roof gardens will probably help give you ideas as well. Just remember that whatever you plant should be about 2 zones hardier than where you actually are if you want them to survive the winter in pots.

Good luck and let us know what you decide to do.

Thank you so much! This is a lot of information to digest through. And you are right, I am planting these arborvitae in pots for privacy. Regardless, I will need to rethink my strategy. Thank you, again, for the thorough write up, much appreciated.

A couple of things I forgot: there's also a conifer forum here and they may have folks who can suggest good evergreens for pot culture in your area. You'll need to be able to tell them about temperatures on your patio as well as wind conditions and light levels. They may also be able to suggest a good fertilizer regimen as you can injure the plant with either too much or too little. I know very little about growing shrubs of any type in pots as they'd have to be super cold hardy for them to survive around me.