Once my feather fletches get completely soaked (shooting frogs) they never lay the same again; it does not seem to affect arrow flight, but they don't look very pretty. Is there anything that can be done to restore them?

Try steaming them over some boiling water, slowly rotate them over the pan 4 inches or so in the steam. They will be as good as new in no time.

You can also wash them in hot soapy water to get crud out and steam them to fluff them up.  This will, however, remove some of the oils in the feathers.

I do like adeeden If they are just wet but I also strike my palm with the shaft briskly while steaming.
Sort of steam, then strike a couple of times, then steam and then strike again. The impact seems to get the feathers back to their original position more easily. When I am almost finished, I wave the fletching quickly back and forth, fast enough to make a swishing sound. It works for me.

When they have animal fat and/or blood or other sticky dirt that doesn't just rinse off, I do like Dave.

Thanks guys!

I rub them the "wrong" way so all the fletch gets separated, let them dry, then zip the fletch back up by rubbing the "right" way. Best I can explain it.

i do like Mr jeffer as well.
i do alot of stumping, and its really nasty and muddy here in St.Louis now i get them wet all the time . just slide your finger down the arrow "feather" backwardsslice the air a couple times to get most water out .
then drying them is my favorite part, i use an air drying method "i shoot the heck outta em till there pretty   "

I get a pressure cooker(without the little pressure thingy) or steam kettle and put the messed up fletching over the little hole that is blowing steam. The pressure pushes the fletching back into shape real fast. Gary

put arrow between my hands and rub them... arrow spin dries....then go shoot them.... They be fine