It seems to me that if I play Italy right, I should almost never lose Rome.
For example,
by turn 4, land at least one unit in Gibraltar.
If Gibraltar is taken, move a destroyer to SZ 92 in turn 5 and begin turtling with infantry.
If 92 taken, move destroyers to SZ 93, 94 and continue turtling with infantry and tanks in turn 6.
If 93 taken, either attack with fleet and fighters and Tac bombers, or just turtle in Italy. Also, move a destroyer to SZ 92 for good measure to cut off any movement by the American fleet, which has now been out of any serious combat for 3 rounds, and if the Axis aren’t kicking butt by turn 7, they never will.
Of course, none of this will work if Italy loses its fleet early on, and it may be cut short by a round if UK sends in bombers in turn 6 to clear the way for the US (bombers land in Gibraltar). But that Italian land force should be sufficient to hold back the US’s first round of assaults and the time spent by the U.S. fleet in the Med buys more time for Germany to take Russia.