When in theme Plugins page I try to update Slider Revolution plugin it does not updates and in WP Plugins page it says that this outdated version is at High security risk but it has no option to update it there.
Is there any error message when you try to update it through Betheme -> Plugins?
If yes, can you send it, please?
Also, did you try removing SR and installing it again?
"Is there any error message when you try to update it through Betheme -> Plugins?" - no errors, and at first look it seams as plugin is updated but when you reload the page the Update buttons comes again and in wp plugin page it also is shown as not updated.
"Also, did you try removing SR and installing it again?" - if I do so, the already set up sildes are not going to be deleted?
Reinstallation will not delete your sliders. They are stored in the database, so if you did not modify the db, nothing will be deleted.
You can also export your sliders for safety, so you will have a backup to import them again.