To put it quite simply, there were very few advantages for Hitler in invading Spain and the effort outweighed any potential results. We must remember that even in 1940/41 prior to the invasion of the USSR when the invasion of Spain would have been most feasible for Germany the German military was already quite tied up. At one point or another they had fought or were fighting in France, Greece, Crete, Yugoslavia, North Africa, Denmark, Norway etc and had occupation forces in these countries. Add onto this the huge manpower and material draw in preparations for Operation Barbarossa there really wasn't much capacity to open yet another front in attacking Spain. Fighting even a diminished Spanish military through the Pyrenees would undoubtedly have been a difficult slog for the Germans and would divert precious resources away from the other fronts. Franco actually pre-empted this by stationing field armies in the Pyrenees to deter any Axis aggression as interest in Gibraltar grew during 1940.

The only real value Spain held for the Germans was access to Gibraltar and the potential for naval and air bases in Spanish Morocco or its various island possessions. Tactically and strategically it was pretty insignificant; Spain was in economic and material ruin after the Spanish Civil War so there would have been little material advantage gained. Hitler did float the idea to Franco of allowing German troops onto Spanish soil to attack Gibraltar in 1940, and a plan was created, but Franco demanded Spain receive the French North African colonies which at that time belonged to Vichy France so nothing was ever agreed. Hitler, in general, had little interest in the Mediterranean and wanted to focus on the USSR by early 1941; he had little interest or ambition to invade Spain, especially when Hitler had been a key influence in Franco gaining power during the 1930s.

The Germans recognised the advantage of having the border with Spain maintained by a neutral, but nominally sympathetic, national leader like Franco. They could continue to trade for vital resources without a costly occupation, long military campaign which would have upset the timetable for Operation Barbarossa and a huge coastline which would have needed to have been protected from Allied attack. The Spanish, if attacked, would have undoubtedly joined the Allies which would have put greater resources into the Allied war effort against the German military. Spain overtly aided the Axis in exporting vital materials such as tungsten, iron ore, lead and mercury and any invasion would have hugely disrupted this supply.