The game doesn't save your progress, you have to beat a co-op level entirely in one sitting.
To continue on the level you left off at, you must choose that level from the settings menu. You can choose and play any level you want in any order you want, also.
BS! I am so sick and tired off these azzhole game companies. Why do they ever bother offering a half-baked split-screen co-op when they obviously could not bother less about completing that part, reminds me me off COD World at War, there you would have to play for 6-8 hours straight or you would loose all and start all over! I say Class Action lawsuit for advertising offline co-op where users off course would expect it will save the progress.