For starters, if the main isn't sheeted tightly, you will definitely have difficulty tacking in any kind of wind. Under most circumstances, it is important to have the main sheeted firmly when tacking.

You should be able to tack in heavy air even if the boat will not carry all the way through. For starters, as you turn up into the wind and get nearly head to wind, the boat may stop - this is OK! As skipper, you need to keep the boat turned into the wind but watch the water flow over the rudders. As soon as the boat begins to sail backwards, reverse the rudders to back the boat onto the new tack. It will also help dramatically if you have the crew leave the jib sheeted on the wrong side for a second or two (backwinding the jib). This will cause the nose of the boat to swing around more easily on the new tack. Ease the mainsail as the boat goes through the wind, quickly get the jib to the correct side, and continue to bear away in your turn as the boat begins to move forward again.