I am trying to root a limb from an apple tree we had to take down. For 1 day the limb, about an inch in diameter and 6 to 7 inches tall with leaves, was in a bottle of water. I then dipped it in root enhancer and planted in a small pot in peat moss. It was doing well until about 2 hours ago. The leaves are limping. Help? What causes this? The peat moss is damp to the touch but not soaked. Please help.
I have done the same thing with a Gala apple tree (of which its parent was invaded by a bug ). I cut it clean off with 3 or 4 nodes, then dipped it immediately, before any air could start to "fix" the wound. I did not put it in any water, but immediately dipped and stuck it in my pot of soil. It was a mix of organic compost and the same dirt the parent tree was. It did look awful for a few days , but I let it set and recover on its own (transplant shock). It did recover! ( yay). Maybe, give it time and care and let it" adjust" for several days if not weeks. But in my mind, putting it in water immediately after cutting, is what "glazed over" the wound (cut), and is not not letting anything in.
If it gets worse, try to re-cut the cutting, dip it in rooting compound, stick it in its own pot with fresh good soil and keep it moist ( not wet). Good luck. I know I'm always disappointed when things like this happen.
There are two ways of propagating trees through cuttings: (1) with softwood or (2) with hardwood. Both methods are difficult, and depend on the tree species if it will work or not (some trees are easier than other, think of e.g., willow which is easy).
Soft cuttings are used in summertime, and are usually small cuttings (smaller than yours, 2-3 leaf nodes) of new grown (green) parts of the tree. You'll have to put them in soil and pack them with transparent plastic so that the air surrounding the cuttings will be saturated with water. This will prevent too much evaporation, which is a problem in your case judging from the photo.
The hardwood method is done in autumn or winter, when leaves have fallen off already. Here you take woody branches of the tree, and cuttings can be a little bit bigger (about the size of your cutting). Then also put it in soil, and a plastic cover is not necessary. In springtime, if still alive, new shoots and roots will grow from the cuttings.
Your plant looks like a hardwood cutting, but then taken in summertime. The leaves are wilting, because the cutting can't take up water from the soil (it has no roots yet), but it is evaporating all its water through the leaves.
Both methods are difficult, and on internet there are many instructions of how to propagate through cuttings. My advice is to read them, and follow the instructions.
A better approach to this might have been to graft the cutting into an existing tree or rootstock. Most commercially grown apple trees are the product of grafting, firstly because trees do not come true to type and tend to revert to being crab apples if grown from seed, but also because the desired characteristics of rootstock may differ from those of the fruiting wood. For example this is how you get dwarfing varieties of a given cultivar, and is and also used to improve disease resistance.
A note on taking cuttings further to the advice already given: plants transpire (and therefore lose water) primarily through their leaves, so cuttings should have all but one or two pair of leaves carefully removed before planting.