After Operation Catapult, the Vichy French bombed Gibraltar. If they could do so, then there were French airfields in range with aviation fuel. Don't you think that the Germans might have put pressure on the Vichy French? The aircraft could have loaded up in Italy, flown to French North Africa, refueled, then headed to Gibraltar. Some reinforcements and supplies could have been flown in on other aircraft. Italian subs could have been used, even fast Italian DDs much like how the Japanese used them.
Without getting into much detailed research, from wikipedia:
The British garrison: Spring 1941
2nd Battalion, The King's Regiment
2nd Battalion, Somerset Light Infantry
4th Battalion, The Black Watch (from July 1940)
4th Battalion, Devonshire Regiment (from July 1940)
3rd Heavy Regiment, Royal Artillery, with 8 x 9.2 inch, 7 x 6 inch and 6 x twin 6 pounder coast artillery guns
10th Anti Aircraft Regiment, Royal Artillery, with 4 x 3 inch, 4 x 3.7 inch, and 2 x 2 pounder anti-aircraft guns
82nd Heavy AA Regiment, Royal Artillery, (from July 1940), with 16 x 3.7 inch guns, 8 x 40mm 40mm Bofors AA guns and radar
3rd Searchlight Battery, Royal Artillery.
"Special Detachment" of No. 1 Tunnelling Company, Royal Canadian Engineers (from November 1940)
No. 2 Tunnelling Company, Royal Canadian Engineers (from March 1941)
Royal Engineers, Royal Signals and supporting arms.
Until the reinforcements arrived in July 1940, there was not much anti-aircraft artillery available. Those could have suppressed along with the coastal artillery by the Luftwaffe. I do not know exactly when those reinforcements arrived in July of 1940 but after the debacle in France, how well were they equipped?
Seek peace but keep your gun handy.
I'm not a complete idiot, some parts are missing!
“Illegitemus non carborundum est (“Don’t let the bastards grind you down”).”
― Julia Child