People have been preaching the death of Pentax since well before the advent of the internet. Regardless, it hasn't happened.
Pentax is not a huge company with a significant market presence. However, they have *a* market presence and they make enough money to stay comfortably afloat.
Once you get past the speculation (which there is a lot of) the actual picture is that there may be ups and downs, but Pentax and the K-mount aren't going anywhere soon. The finances aren't world-beating but they're certainly viable. With the K-7 and now the K-x (which is already a surprise hit), the trend may start heading in an upwards direction rather than maintaining its previous flat line.
Pentax gets a bad rap. For example, "behind a generation in ISO noise." The K10D used the same sensor as the D80. The D80 got the reputation for low high-ISO noise. Actual users found that in RAW the difference was negligible and the K10D was in fact cleaner at low ISO (and currently has a following for that characteristic). Similarly, the K20D got a reputation for being noisy, particularly from tests like dpreview's, which clearly showed a higher level of noise from the K20D but also much better detail retention, implying that it was simply using less NR. Nonetheless, in the absence of RAW testing at that time, the competition was declared superior in low light... until they threw K20D RAW files into the DPR tests of the newer K-7 and found that, in RAW, the K20D was cleaner than the next-generation Canon and Nikon semipro models that they praised so highly.
People claiming that Pentax cameras yield noisier images or sub-par overall IQ simply don't know what they're talking about. I owned and got a lot of use out of the highly regarded Canon 40D, and bought it expecting something special, but found the images consistently dissappointing compared to the output from my old K20D. I now own a K-x which trumps the 40D in all areas of image quality and is on par or better than the K20D in most.
Some criticisms do have a legitimate basis. The autofocus on my K20D, and the pentaxes that preceded it, was pretty dismal in terms of speed, relatively speaking. My 40D was light-years faster and worked better in low light. However, it got the job done, and AF performance on the latest models (K-m, K-7, K-x) is vastly improved. In most conditions there's no functional difference in AF performance between my K-x and the 40D. Both are fast and positive and can't track worth a darn.
Pentax does need to address the fact that autofocus with their top-drawer "SDM"-motor lenses is slower than their traditional screw-drive lenses, which is a shame since they're such fantastic optics.
QC is another issue: There were sensor issues with a lot of early K-7's, and us K-x early adopters are dealing with an irritating battery issue. Fortunately, Pentax is responsive in providing solutions to the problems that arise. It'd be nice if they didn't happen in the first place, though.
Third-party support is, indeed, more limited. Unless you have specialized needs, however, you should be able to find what you need.
I can think of a number of good reasons for Pentax. If you like the smaller form factor, the K-7 is on par with the competition's semipro models performance-wise (give a little, take a little) in a much more compact package that just happens to be the most rugged in its class. The K-x is a great little entry-level camera with a new sensor that turns out fantastic results from an even smaller and lighter package.
The lens line-up is made of some pretty strong optics and has some uniqueness as well, seen most clearly in the compact "limited" primes. Pentax glass used to be the most affordable on the market as well (the FA 50mm f1.4 went for not much more than the competition's 50mm f1.8s and performed admirably) but the changing values of the dollar vs. the yen and hoya's odd management practices have brought prices up a bit, to be a bit more level with the competition. There are a lot of truly fantastic barely-known lenses in Pentax's stable that get people hooked, and even when some of them buy into full-frame systems and the like they tend to hold on to at least one Pentax to mount their FA 43mm or FA* 85mm on. There's something magic about a lot of their lenses.
Unless you need specialist lenses or the sort of support networks Canon and Nikon have set up for pros, there's no reason not to give Pentax your serious consideration. They make excellent products that produce excellent images in the right hand and have both advantages and disadvantages against the competition. They are not going under anytime soon.
For the sake of disclosure, I am a fan of Pentax. I'm a fan because I've used their products and experienced how good they can be. I am also a fan of Canon, Nikon, Sony/Minolta, Olympus, Panasonic, and Fuji DSLRs and lenses. I would own and use all of them if I had the money and time. I have owned cameras from Olympus, Pentax, Canon, and a bunch of others from the film era. Anyone who tells you that any given brand is a bad idea (unless for a very specific reason) is either misguided or full of crock, in my opinion.