Gary Grigsby's War in the West
Which version of the game are you playing? I found that the more recent betas and the latest official version (1.02.35) improved the performance of the auto naval patrols somewhat over the original game version.
However, it is important to spread the squadrons around the Med as you advance, including the fighter squadrons that belong to the Coastal AF and the Malta Air Command. The fighters will intercept the Axis naval patrols, which contest control of sea hexes. I tend to set custom naval patrols just to cover invasion and beachhead areas, or to isolate Axis ports that are otherwise cutoff. The auto naval patrols have given me control of a band 3-4 sea hexes wide all along the African coast; once I occupy Sardinia, this control extends over most of the western Med, except in bad weather turns; the same goes for Sicily.
Also, hit key Axis ports with port attacks (port targets are available in either city bombing or ground attack). The ports contain Axis naval assets (small patrol boats), which also exert control over nearby sea hexes. The more damage a port suffers, the less control it can exert over nearby sea hexes. This seems to work particularly well in the English Channel - I have been able to maintain control over most of the Channel sea hexes all the way to the French coast by targeting the French Channel ports with Typhoons and Mosquitos from the 2d Tac AF in 1943. I assign 2-3 strikes per day of approx 50 FBs each, 2-3 days each week; I lose some Typhoons and Mosquitos, but the pilots gain experience for almost a year before the big invasion.
Finally, recon Axis airfields to look for bombers, then bomb these airfields - you want to limit the number of Axis a/c available for their naval patrols.
I recently read Samual Eliot Morison's account of the Sicilian and Italian invasions - the Allied invasion forces suffered quite a bit from Axis air and naval attacks (by small patrol boats).