Calendar apps and certain to-do apps allow you to set deadlines for your important non-urgent & permanent notifications. Instead of only letting you delete or archive the item (e.g. a note, an email, a chat notification), it could also give you the option of receiving reminders of the deadline some time before it actually arrives. As for the convert to permanent action that I suggest for important non-urgent & transient notifications—temporary bits of information that you don't want to lose—we have a few partial solutions.