I've been trying to conquer my fear of working with yeast — so far, so good. But one thing I've noticed is that when I punch down the dough after the initial rise, it is so hard to roll it out. It always recoils or springs back a little bit. Does this mean that I need to knead the dough more? It doesn't seem to have any effect on the final product, but I'm just curious.
Liz, it's hard to say without seeing your recipe or process up close. How soon are you rolling the dough out after punching it down or kneading, and what are you rolling it out for? Pizza? Cinnamon rolls? Calzones?
In any case, our guess is that you need to let the dough rest for a little while after handling it. When you handle dough, including when you knead or punch it down, the gluten contracts and seizes up. It gets stiff and needs to relax.
There will always be some springback when you roll out a yeast dough, but if it's well-raised and rested it should roll out quite thin. We notice this especially when making pizza; when we handle the dough rounds too much they get stiff and stubborn. When they relax they stretch out easily.
When you let it sit and relax, the dough becomes much more pliable and stretchy. Try letting your dough rest for 20-30 minutes before trying to roll it out.
(Photo by Faith Hopler)

Red-and-Pink-Stripe...

because you have weak hands.
sort of an unnecessarily mean comment or a very bad attempt at humor...
I saw the first post and was going to say that you need to let the dough rest for a little while. That generally works. If time is an issue, even a few minutes will help.
What about store bought pizza dough? I had a similar thing happen when I bought pizza dough at whole foods. Should it be left to be room temperature before rolling it out? Does it need punched down? Unfortunately, when you buy it there are no instructions on the package.
Well if it is pizza type dough, here is how you handle it.
Mix the dough
Cover it and let it rise 30 minutes
Cut to size and roll into a ball
Cover with olive oil and cover
Let it rise again till double in size
Use it or stick it in the fridge.
Wow! Look at all that houska dough! Delicious.