Probably rotting off at the base of the stem. An otherwise healthy-looking plant will keel over and obviously wilts pretty fast. I've been having terrible problems with New Guineas doing it this year. Try to keep the surface of the soil dry, don't overwater. You could also try removing the surface layer of soil and replacing with fresh stuff, or laying down a gravel mulch.

Wilting can also be caused by underwatering, too much sun, mites, or aphids. If you have an insect problem the plant can continue to wilt despite watering and eventually you end up overwatering and killing the whole thing.

Shrubs n bulbs, You described exactly my problem. The rot was at the base of the stem. I pulled all of them out and will try again with fresh soil. I can't see any mites or aphids and I'm pretty sure too much sun is not the problem. These are regular impatiens (not New Guineas). Do you think the wilt is contageous to my other impatiens?

The fungus that causes this rotting is present everywhere, but obviously letting it grow on a plant could cause more spores to be around. You can actually save plants like this by snipping them off a little above the rooted part and rooting them as cuttings, but this is a lot more trouble than just buying more trays.

This fungal problem can really be a pain in containers. You need enough drainage holes so the plants are not sitting in waterlogged soil for lengthy periods. Do not use garden soil at all as it is heavy and already contains a high pathogen load - use fresh soiless potting mix. Always start with a clean container and add a liquid fertilizer to your water unless it's already added to potting mix. Coninuous heavy shade will also increase the tendency toward this problem as it slows drying time. Good luck!