Here's what they had to say:

"Changes in Visa and MasterCard's policies toward third-party processors who operate domestically in the U.S. have had the effect of 'culling the herd' and eliminating the weaker, more dangerous and unreliable processors from the market. In this sense, third-party processing is a much more stable industry. Some of the unintended consequences of these actions has been to increase the number of disreputable processors who operate in regions where MasterCard and/or Visa don't have as tight a control on member banks. So my answer would be a qualified 'yes' given these facts."
— Jack G., CEO and Co-Founder, ClearCard.com/CNWB.com

"Third-party processing is a very safe, secure and intelligent way to bill for your paysite. It is preferable to a single-site merchant account as using a registered IPSP in the U.S. or EU, and it allows you to remain compliant with the rules of Visa and MasterCard and to dedicate your efforts as a program operator to doing what you do best: selling your content to members. In my opinion, the safety of using one of the three IPSP's (CCBill, Epoch and now 365 Billing) in the U.S. or EU has never been more assured."
— Chris Mallick, CEO, ePassporte

"I don't think that third-party processing per se has ever been 'unstable.' Rather, there were a number of companies engaged in it that were unstable, meaning they weren't very good at it and had poor practices and standards resulting in business difficulties or problems with Visa/MC and/or their banks. At this point, I think that most of the more unstable players have been forced out of the picture by these pressures, although it's still important to choose a processor carefully."
— Ron Jenkins, CEO, DHD Media

"Not really. The key is to choose who you work with and to understand who they work with. The rules are pretty simple, and when you start to hear crazy stories about a billing company, it is crucial to verify them. Chargebacks are here to stay, and if a webmaster decides to trust a billing company with its revenue, a minimum of research is in order to have an idea about the business model of that company. Everyone wants aggressive billing, but it has to stay within the limits."
— Nancy Moore, Account Manager, GammaCash

"I have to say, I really do. However, as more and more banks dropped adult, things have started to convene to a few single banks still willing to take on high-risk accounts. Thirdparty processors who have been following the rules for many years and who have established solid bank relationships are in prime position to stay in the game, and we have noticed them recently overtaking merchant accounts in both reliability and performance. I think as people begin to see this, they will start to lose their biases against third-party billers and slowly migrate to them."
— Keith "Varius" Bussey, Head of Special Projects, IwantU.com

"I think third-party processing has been filled with stories of disaster, and now we are down to only a few viable alternatives. The old rule of 'only the strong will survive' is particularly true here. I have a long history with CCBill, and they have proven that they are here for the long term. Slow and steady wins the race!"
— Steve Lightspeed, Founder/CEO, Lightspeed Media Corp.

"The answer should come as no surprise. Without a doubt, third-party processing is more stable today than ever. Managing credit and chargeback ratios and avoiding penalties and fines has become as much an art as it is science. The well-established billing companies have a considerable advantage to new companies not only in the matter of risk management but also in credibility."
— Rand Pate, Director of Communications, Epoch/Paycom

"From our point of view, we feel that stability has increased considerably. The main concern of merchants when choosing a third-party billing company is whether they are going to get paid on time, every time. Let's face it, there are only a few third-party companies that have direct relationships with the acquiring banks, and the balance depend on ISOs for placement. When choosing a third party make sure that the comfort level is there and all questions are properly answered."
— Norton Burah, President, myVirtualCard.com