Yeah, they absolutely do; they need to stay connected to power so that the card controller can, over time, move the data around. The storage cells work by being charged up, and the charge leaks out again. If the card isn't powered, this can result in data loss.
It has a lot to do with how hot the card was when the data was written. Weirdly, the hotter the better. You want the chipset cool so it runs well, but you want the memory banks hot while being written, but then cold while being stored.
This link has some data:
https://www.partitionwizard.com/clone-d ... orage.html
Search for "Is SSD Good for Long-Term Storage?" The table shows that if the SSD is stored, without power, in 55C heat, then data can be lost in just a week if it was written at 25C, and can be lost in 8 weeks if it was written at 55C.
On the other hand, the best case in that chart is writing at 55C and storing at 25C, where data can last over 400 weeks.
This link has more graphs, from a different vendor, but showing roughly comparable figures:
https://www.anandtech.com/show/9248/the ... -retention
Regardless, the underlying lesson is this: cards and SSDs that are not connected to power degrade. They can degrade very quickly in hot temperatures. Their retention will be fine as long as they have power, as the controller can detect the weakening charge and cycle the data to different cells, starting the leak time over again.
You should expect SD cards to be markedly worse than this; SSDs are built to a much higher quality standard.
Hard drives, on the other hand, deteriorate extremely slowly. The failure point there is that the drive might not spin up after being stored a long time, as opposed to the magnetic media losing its charge. You can stick one on the shelf and usually leave it there a decade. This, IMO, is a *much* better place to put your save games.