A quick read from Matthew Lyon, “Forget This Device“, where they dug out the reasons why so often the simple little affordance some log in prompts have of “Remember me” or “Remember this device” end up being utter BS. A lot of the reasons basically come down to poor implementations, and outdated approaches to cookies (most browsers don’t store cookies from other domains at this point, as a default security measure… guess what a lot of authentication prompts use to store your login). It’s not an exhaustive list, but if you were ever curious, it gives a nice breakdown of some of the common reasons.
Next step is convincing developers to fix those problems.