Thanks to all of you for the great advice. I've learned so much from this forum!!!

My bike did sit unused for 5 years, unfortunately, and endured an interstate move and a few months in storage during that time. BUT I had it thoroughly checked out and tuned up back in April, when I was ready to start riding again. So I am thinking the bike is probably fine and its me.

On this morning's ride I hit the less severe of the two situations in which that usually happens to me. I shifted to the middle ring halfway down the downhill, and then as soon as the little dip at the bottom of the hill started to turn uphill I shifted to the smallest ring. The chain made a little noise for one revolution but then shifted, and then my climb went smoothly! I didn't like giving up my pedaling power on the downhill by downshifting early, but it was worth it to be able to get into my lower gears when I needed to without serious problems. I should hit the other hill, the 20%+ grade, tomorrow morning, depending on the weather, and see how that one goes.

You ladies are the best. Thanks!