I hate to be the bearer of bad news but I had the same symptoms on my 85 suzuki 55hp with oil injection. The upper oil injector line over the years had become stiff and had shrunk. When the engine warmed up it popped off. Without oil the one piston temporarily seizes and when it cools it loosens up enough to start. If the engine was run long enough in this condition you'd find a serious lack of compression in one of the cylinder. I should have replaced my oil lines every five years or so according to the dealer.

Check all the oil injector lines and look for a leak. Have the compression checked on all the cylinders. Most likely one is low. If I had replaced the injector lines I'd still be running my engine although it did give me an excuse to upgrade to a new 4 stroke. Hope I'm wrong in your case but I had the identical thing happen last summer.