This seedling was green and standing upright the day before this picture was taken.

What are you growing them in?
When they're out for 2 hours are they in direct sun?

Are they bone dry before you water? If so you may want to water a bit sooner.

In addition to Bill's question, how are you fertilizing?

Josh

They are in organic seed starting Jiffy Mix. They are in direct sun. I wait until they are bone dry, but will water sooner if that helps. I have not added any fertilizer.

Get them out of direct sun, keep them consistently moist but never "wet," and begin applying fertilizer at 1/4 strength dose.

Josh

I've found that seedlings grow better in a blend of organic potting soil, compost, and vermiculite. Those commercial mixes usually use soluble fertilizers that wash out when you water the seedlings.

Always give pepper seedlings time to get used to direct sun if you grew them on a windowsill. That may take a week or more.

looks like a lack of water you should try to keep your pots a little more moist but not soaked they are still to young to take the stress of running totally out of water looks like that could be happening using them peat potters outside will dry out very fast your better off putting them in small plastic cups IMO