Laura Ries' latest blog entry squarely addresses the issue of what to do about brands and product categories that are dying. The thrust of her advice is to avoid the natural inclination to try to preserve a dying brand by modifying it.
A strong brand stands for something in the mind of the consumer. Years of consistent, focused marketing and a remarkable product or company are the typical recipe for a strong brand. But sometimes the entire product category becomes obsolete, and the once-strong brand dies with it.
The natural inclination is to try to preserve the brand symbols (name, logo, etc.) since so much time, effort, and money went into making them powerful and well known. So why not transition into new or evolved products and attach the same brand to them?
Changing your brand is like trying to change the meaning of a word. If a word is relatively new and not well known, then it's not much of an uphill battle to assign a new meaning to it. But good luck trying to change what an old word with an established definition means to people. You're much better off inventing a new word.
Ries gives numerous examples of ill-conceived attempts to preserve or modify brands.
When your brand is dying, resist the temptation to modify it. Spin off a completely new brand (and not an extension of your current brand). It will take time and money to build it, but at least your new brand won't be doomed to failure.