I'm no expert with impatiens but I think the biggest mistake people make is watering them too much. It is not unusual for them to drop their blooms when you get them home. It seems like any change in their environment will have them dropping blooms/buds. But they will come back.

Do you think they might be too wet? Let them dry out between waterings. It almost looks like the leaves got wet and then they got some heavy duty sun and they burned a bit? You can pinch back anything that doesn't look good.

Great pictures by the way.

Do you think any of the above may be happening?

What did they look like when you got them?

I watered them right before I took the pictures, so that explains why they appear wet. I have been watering them every day since I keep my apartment relatively dry (~40% humidity), and impatiens apparently like humidity. I have no idea how much is too much, though, so I'll try cutting back on the watering and see how they react.

These plants have not ever been exposed to too much sun, as I have a north-facing balcony in Wisconsin, and they are usually indoors anyway.

The plants were all doing well when I got them--they all had blooms.

Now the situation with the plant I didn't photograph is getting dire, because the stem has collapsed, and all the leaves are covered with light brown splotches on their undersides. Is this one a goner?

I think you are keeping them too wet- liking humidity does not mean liking soggy soil.
Place the pots of a pebble tray to increase the humidity but don't water them until they need it.
Stick your finger in the soil and feel it.