By John TantilloMarketing Expert/Founder and President, Marketing Department of America

As if to prove that not all publicity is good publicity, we've got David Letterman.

David Letterman is a man who has consummately built a brand right on the edge of good taste.

He's no shock jock, but he has always been able to say outrageous things, push the envelope and basically get away with it night after night.

But not this time. The Sarah Palin flap shows a real weakness in the Letterman brand: his edginess and his inability to genuinely apologize.

Of course, the edginess and the inability to genuinely apologize is part of his brand, and therein lies the problem. Asked to apologize, he did so, and then made more jokes, because his snide, nothing-is-really-serious brand is at odds with the need to sometimes be sincere. His edginess attracts viewers, but it has also led to conflict over the years (Oprah, Madonna, John McCain, et al.).

A great brand takes years to develop, but a single bad step can be fatal. Of course, whenever you examine the reasons behind the decline of a brand, you will almost always see that the flaw was there for years, and the single step was really just the last in a series of missteps.

With Letterman, the recurring flaw is arrogance. As one of our few media "institutions," he has adopted an "I-can-do-no-wrong" attitude, which is never good for a brand. The most successful and enduring brands remain responsive to what the consumer wants throughout the life of the brand.

Bottom line: when a brand has done wrong, it must make a clean break and apologize. There's an important update on the story: as of Monday night, Letterman has turned around and delivered a much fuller apology, with no apparent sarcasm.With people rallying outside his studio for his head, Letterman had to do something, and it looks like he did.

We'll see if it calms the outrage. The apology sounds like it hit exactly the right notes, but it comes at least a week too late.

From a brand perspective, I think the damage has been done. At best, it looks as if Letterman was uninformed (i.e., his claim that he didn't know which daughter he was talking about) and arrogant. It might not take as much as you think to have Letterman's image suddenly stick as that cranky old guy. This would be the kiss-of-death in the highly competitive late night talk show arena, with Conan O'Brien poised to take the younger demographic away.

Fact is, the next step for Letterman is to sin no more and remember the viewers who put him where he is today (and can take it all away).

And remember, things are always easier to understand when you keep marketing and branding in mind.

John Tantillo is branding editor for Fridge Magazine, the magazine for small business owners and entrepreneurs. He is the author of "People Buy Brands, Not Companies."