Chosen Solution
A Mac Mini I have wasn’t saving the date and time/wifi so I ordered a new PRAM battery. I put it in but the date and time/wifi still isn’t being saved. I flipped it around but the same issue occurred. I have pushed the metal fingers as close to the battery as I can, yet it still wiggles a little bit, so maybe that’s why? I tried it on another A1176 I have and the same problem.
Before you return what sounds like a bad battery, open up the date and time preferences and make sure you have the “set date and time automatically” checked.