According to Smart Money Magazine, cost is a big factor. There's always been a price premium for convertibles, but that gulf has widened over the years, and it's not like there's very many affordable conertibles in the first place. Age is another reason. While Baby Boomers still like covertibles, their kids, Generation X and Y, seem ambivalent. Compounding those factors is a sluggish economy that has buyers focused more on practical cars that don't break the bank than splurging on some kind of roadgoing confection.
We might also suggest that given the frosty global economy, we're also seeing fewer new convertible models go on sale in volume segments (exotics seem to be immune to this trend). And since convertibles, like coupes, tend to have particularly short sales lives, we're not terribly surprised to learn that sales are down.
But it could be a vicious cycle – there less demand for a bodystyle that's not as popular as it once was, and those models that remain tend to be pricey. That doesn't mean that the convertible is dead – that rumor has failed to stick in the past – but it does suggest that automakers are likely to stare even longer at the beans they are counting when figuring out whether there's a business case for a new convertible.