Xbox profile can’t sign in to xbox live on 360 games

I’ve been seeing people with this problem as well where you can’t sign into xbox live on 360 making you not be able to play anything online. Any video I find to help either requires me to delete my profile and sign back in, or clear all local xbox 360 storage and I don’t want to do any of those because people have been saying that when they deleted their profile that they can no longer sign back into it and that when they cleared xbox 360 storage they lost all pfps and saves they had. Anyone knows how to fix this problem?

:)