Here's what I did after I found out that Mevio no longer exists. (You can check Wikipedia or Google it.)
1) In iTunes (podcasts list) I did a search for Mevio, and some Old Time Radio Comedy podcasts showed up. I had never subscribed to these podcasts, but had downloaded 7 about 5 years ago.
2) I copied them to a new folder on my desktop (but not the mother folder).
3) I deleted the podcasts from iTunes, along with the mother folder. I checked and they were all in the Trash, and I verified that my new desktop folder still held my 7 original podcasts.
4) I dragged these 7 podcasts to the upper side of the sidebar and they were re-imported into my podcasts in a "new" folder, Old Time Radio Comedy. There is no longer an i button for information (that previous gave the Mevio url).
My podcasts have survived, and I no longer get that annoying log in window 4 times a day! Whew!