There are usually two culprits - the frying oil or the dredge. To prevent this, start by dredging your cube steak thoroughly. First in seasoned flour, then the egg mixture, and back in flour, pressing the coating firmly onto the meat. Let the breaded steak rest for a few minutes before frying; this helps the coating adhere. When frying, ensure your oil is hot enough (around medium-high heat) and avoid flipping too often - once per side is usually enough. After frying, let the steak rest on a paper towel-lined plate before assembling your sandwich.