So besides logistics (Ethiopian troops would be without considerable resupply for at least a year even if the Italians overwhelmingly won because of poor infrastructure and the British wrecking Suez as bad as possible), there's no way Mussolini would make peace with the Soviets. Here he has a golden chance to wipe out Communism once and for all, there's no way he wouldn't take that chance. Sure, things might still go south in the East, but Mussolini would try his damnedest. He didn't send troops to Russia OTL for no reason.
Then there's his idea that the WAllies would throw in the towel (they wouldn't). This is an alliance who continued on after losing its foothold on the mainland (including their strongest army by far at the time), and who took the full brunt of Japan's overwhelmingly successful opening moves and didn't flinch in terms of determination. Sure, losing Suez and Egypt would be hard on British morale, but all that'd result in is Indian troops flooding Iraq to push the Italians back.
Then there's D-Day... That wouldn't have happened without the Med front or Italy, at least not for a while longer. The Allies used the Med as a testing ground for everything they were to use for D-Day. Without those, Eisenhower would be a lot more cautious about invading Europe.