I've been using / fixing / buying chainsaws for years, and while I'm not a professional, I do consider myself slightly more knowledgeable than the average guy when it comes to saws. I am a die-hard Stihl guy, but I've had a couple of Husqvarna's over the years. A couple of questions for you:
1) Don't take offense at this first question, but are you SURE that you are tightening the bar appropriately using the 2 lock down bolts AFTER you adjust the chain adjuster screw?
2) Are you SURE that they gave you the right sized chain? A neighbor of mine bought a brand-name saw from one of the big box stores and it came with the wrong size chain. The LENGTH of the chain was right, but the pitch wasn't. When people buy replacement chains, that's a common error, and almost always leads to chains that come off or slips even when they appear to be properly tightened. Your chain for that particular Husky should be 3/8" pitch and .050" gauge, with 72 links, I think.
3) But more relevant to your situation, I think is this: If the chain has come off more than 1-2 times already, have you checked the drive links? It is NOT AT ALL UNCOMMON to ruin the drive links if a chain comes off even once. It may not be easily noticeable, but if one of the drive links is even SLIGHTLY bent out of alignment, the chain will come off easily.
4) Less likely, but still possible, is the sprocket on the end of the bar. Does it move freely when you try to rotate it by hand, or does it bind? The sprocket tip might be damaged.
5) The bar itself might be bent ever-so-slightly. Put your chain on and move it by hand and listen to see if there is any "scratching" sound as the chain runs through the grooves. There shouldn't be a sound -- if there is, it might mean the bar is slightly off-kilter or there is a pinch point that is causing the chain to bind and jump.