NOAD says the phrase going strong means "continuing to be healthy, vigorous, or successful," with a usage example of "the program is still going strong after twelve episodes." Macmillan defines it as "successful or healthy, and doing well", with these two examples:
The company's going strong and we expect to do even better next year.
My grandmother's 95 and still going strong.
It's interesting that two of the three dictionary examples have the word still, as many of Xantix's example above also have. That's often the sentiment conveyed: it's now past the time you thought something would have faded into obscurity, yet it continues to endure. In the case of the NPR article, some might be surprised to find the Facebook generation – obsessed with 160-character texts and 140-character tweets – would be hardy readers of those old-fashioned relics we call books, yet statistics show that that generation is reading strong.
I think that the "going" in "going strong" can be replaced with other "-ing" verbs, and the expression retains the same meaning, although in a more localized sense. So, the only way to make, say, listening strong "work" would be to devise a context where it seems surprising that some particular person or audience was still actively listening. One possibility might be:
Even though Lawrence Welk has been dead for 20 years, his show continues to be aired on PBS, and his fans are still listening strong.
Although I'd also agree with Bill Franke's comments above: the expression should be used sparingly, as it could easily be overused, and oftentimes there are probably better ways to convey the same sentiment:
Even though Lawrence Welk has been dead for 20 years, his show continues to be aired on PBS, with a band of faithful listeners tuning in each week.