The United States was able to resupply the Khe Sahn fire base by air during its seige by NVA regulars, but lost some planes in the process. By controlling the surrounding high ground, the NVA was able to eventually shut down the runway, and resupply continued by airdrops.

I don't know if we were conducting offensive air operations from Khe Sahn. I think some Cobras and Skyhawks may have been based there early in the battle, but our supporting air assets from carriers and bases in the south pounded cleverly concealed NVA gun positions, and the seige was eventually lifted.

Earlier, the French had tried air resupply of beseiged Dien Ben Phu and its surrounding air bases, but to no avail.

Earlier still in WWII, the Luftwaffe on several occasions attempted to resupply surrounded troops on the Eastern Front, most notably at Stalingrad. Almost without exception, these efforts were failures, and the cut-off units were defeated.

Probably the most famous air supply mission - although not of a military base per se - was the Berlin Airlift. I seem to recall that allied pilots flew over 200,000 missions in support of the isolated city. Read about the famous "Candy Bomber", or watch for this episode to run again on the History Channel.

sp