Backup the character save files.
Do have more than one save?
I hope you create manual saves and not just use the autosave feature
Does it happen with a new character?
I believe you can refresh the memory cache at boot of the console.
I do not have a console but at least with more information someone with an xbox might be able to offer more suggestions.
Try to clear ther cache before loading any save: https://support.xbox.com/en-us/xbox-360/system/clear-system-cache