There are a few factors you failed to mention, but I would say the first mistake is the peat pots. In the baggies, they tend to hold too much moisture, out of the baggie they will leach the moisture away from the roots and evaporate it.
Some plants will put on new growth well before roots are established under high moisture conditions. What plant(s) are you doing?

I suspect the peat pots are pulling the moisture away from the roots, or the roots are not established well enough to support the top growth when you remove them from the baggie. When you first see the wilt starting to occur, put them back in the baggie, and mist them.

I would recommend that you abandon the peat pots, and use small plastic containers instead. Place the cuttings in a north facing window, or on the outside in full shade so they can get more natural light to begin with. Do not disturb the roots until you can see them through the drain holes. With plastic containers you can remove the plant without breaking the roots.

Agree with Tom_W...might even try using the small clear Solo cups until you get the feel for propagation. You can see the roots through the sides of the little pot and it will fit in your zip locs. Make some drain holes in bottom with a hot screw driver first. If your kitchen window sill is in full sun, you might want to avoid it for awhile until they are acclimated to lower humidity. Peat pots are useful for some few things...not much in my opinion, but I do use them for pre-starting melons and cukes...usually sitting in a tray with some water. You have to peel the sides down when you plant to prevent the wicking away of moisture...and that is out in the garden in damp soil.

Thank you to both of you. I am rooting azalea, a few unknowns from a generous neighbor, bunch of climbing and shrub roses, clemantis (taking forever), v. euonymus (easy - this is what gave me the false confidence), gaura, hydrangea, and pink flowering almond.

I killed the white flowering almond, the weeping cherry tree, purple crepe myrtle, another pink flowering almond...

I don't think that I should move them out of the peat pots at this point to put them into plastic, right? Can I put them on the windowsill with water at the base to compensate for the peat pulling the moisture away from the roots? Or should I just do a mercy killing on these cuttings and start again with plastic?

Stupid peat pots. No wonder somebody gave me >200 for free. I am wasting alot of time and energy.

Thank you again for helping me.
Zophra/ Tamara

clay pots are no better than peat pots.. they wick all water into the atmosphere ... which leads me to the next issue ...

are you running the air conditioner???... are you removing all the ambient moisture in the house for your own comfort???

take your baby from the peat .... or cut sections out of the peat as the roots might be attached.... into a solo cup, only a bit bigger .... then put the baggie back on afor a few days .. they cut open the top of the baggie and leave it for another week ... then try moving it out to a place that has a pebble tray ... etc ..

in other words ... move it slowly into its new humidity .. you cant take it from its wet little greenhouse ... and throw it in the kitchen ...

think aobut it .. and then come up with your own plan ... but all moving has to be gradual .... just becasue you are ready ... doesnt mean it is ...

good luck

ken

I think that if you wean them from the plastic bag SLOWLY, they may survive. ie. open the bag a little bit, wait a few days, then open it a little more, and so on. Some plants can't make the transition immediately from the enclosed hi-humidity plastic bag environment to the open air. I had this problem with viburnum rooted cuttings. Good luck.