There are lots of methods of propagation. Google begonias + propagation, it will take you to a large site with different methods of propagation ; i.e., 'Brads World', 'Martha Stewart', etc. You would be wise to propagate a leaf if you can, it sounds as though the plant is badly overwatered.

First thing is you should repot it again - only go back to a smaller pot for winter (I recommend a clay pot for this type of begonia). The second thing is it is normal for this to lose leaves in winter but the remaining leaves should stay plump and rigid. It can even defoliate completely in winter but do not despair since this is also normal - it is resting in a semi-dormant state so do not quit watering but do not keep it soggy either. Too wet leads to root rot, too dry and the fine roots will start dying and the rhizome will lose water and start dying as well. It is a fine balance at times. A good draining potting mix should help in this endeavor.

If all the leaves are wilted and the soil is wet then I'd say you are close (if not already) of root rot. A clay pot appropriately sized should handle the watering issues (unless the drain hole clogs). Use a fast draining potting mix. Some folks like to use perlite in their mix. I've found that Miracle Gro potting mix (not the moisture control mind you) works pretty good for all my wild assortment of begonias including this very begonia.

For propagation, cut a leaf that is not wilted. If it is wilted you may want to cut it and put it in a baggie or plastic container to "plump" up. If the leaf is wilted then it may not be suitable for propagation. There are many methods to propagate by leaf - entire leaf with petiole and wedge are the ones I have most success with. Jiffy pellets worked very well for me last year and I recommend it highly especially if you do the wedge method. You can buy the pellets with a tray and humidity lid for less than $10. Any good potting mix or straight perlite will also work - do use a humidity lid in winter though. A small pot with a baggie will also work. Water rooting will work as well with the petiole intact (about an inch long) much as you would water root an African violet leaf. If water rooting, do seal the surface of the water from the household air to prevent germs from multiplying and rotting the leaf.

Lastly if the rhizome is starting to turn soft (not plump and rigid), remove all the soil and inspect the roots since rot may already have set in. If this is the case you may cut the rhizome as a last ditch effort to start some new roots on the severed rhizome. You may want to let the cut end scab over for a day before repotting. Place the cut rhizome in a dry container with a lid to prevent germs and also allow the humidity to keep the rhizome plump while scabbing (callusing) over. Rooting hormone can be used but isn't really necessary. Wiggle the cut rhizome with the leaf side up much like an iris rhizome into a small pot of potting mix, water slightly, and cover with a baggie.

Thank you so much! So much information! I will print it out and try the different ideas. Thank you so much.

Lesli