1,008 6 13. add a comment |. up vote 5 down vote. I generally only cook steak medium-rare, and I am able to leave the leftovers in the refrigerator for up to 6 days or so (most recommendations say 3-5 days) and have never had any issues as long as it's wrapped properly.dd a comment |. up vote 5 down vote. I generally only cook steak medium-rare, and I am able to leave the leftovers in the refrigerator for up to 6 days or so (most recommendations say 3-5 days) and have never had any issues as long as it's wrapped properly.