Intro
i want to keep it short so i will say that PS3 launch is known to everyone and even diehard PS fans are not going to call it a success. Many assumed that Sony will exit from this high risk, low margin business. But so far they have not only remained in the race but they are doing ok. i will say its NTS/G state. (not too sorry & neither too good state). Anyway, leaving past and present aside, my point is that why PS3 is going to survive the longest or more than PS2.

Reason 1: Its The technology 
PS2 was launched in 2000 with DVD Drive but at that time DVD drive was pretty common and so within few yrs (2 i think) BD consortium was formed.  At the time of PS2 launch DVD was well rooted in the market. But PS3 which has the BD drive was no where in the market. So it was actually PS3 which introduced BD and also created a market for it. So the technology PS3 has got should help it to remain easily for longer period in the market. 

Reason 2. Games
When PS2 launched all the its major IPs franchises like GTA, GT, FFXIII launched within 2 yrs. or around 2 yrs. But many of these major franchises for PS3 has yet to be released. GT and FFXIII and God OF War III. In my view only 1 major IP has been released on PS3 yet which is MGS4.

Secondly All these games franchises had atleast 2 major releases on PS2. and if we expect two major releases for PS3 for all these franchises than i think PS3 is going to stay for another 4 to 5 yrs easily.

Reason 3. Price
PS2 was launched with a Price tag of $300 and later on it sold most at the price of $200 and then it continued to sell well.. PS3 has yet to hit a price tag of $300, $250, $200 and so on. PS3 has been in the market for over 2 yrs and 6 months and if we assume that it will hit $300 on its 3rd Birthday and then it won't hit $200 before its 5th birthday and if that is the point where it has to sell most than it should stay for some time at $200 price point... and Sony will not like to cannabilize its sale by announcing the next PS too soon. or when it is having most sales.

Reason 4. Developers & Publishers need to stay happy
As the processing technology (CPU like Cell) are advancing so is the programming is becoming complex and more time consuming. It is easy to show that multithreaded processors provide linear improvement in performance BUT only when multithreaded applications are run on it. And multithreaded application are not easy to make or develop, they need time and resources. Right now Sony and its first party studios have developed some very impressive engines for PS3 and the cost on these engines can only be recouped by developing more and more games on it. So it is safe to assume that Sony is not going to bring in another PS too soon in the market, where Sony itself has spend too much resources in its own different engines.

Reason 5. PS3 echoSystem is big.
Sony this generation due to competition and secondly trying to be media center for the living room has made many non-gaming applications for PS3. From Home to video rental and now free music streaming. These applications have just been launched, and i think Sony has plan for many more such applications too. Home still in open beta and starting to show its color like EA Center in Home and other puzzle games in home. It still has not achieved even the fraction of its potential. The games and developers/publishers have just started to use Home and we still are waiting for some true integration of Home Space in games and games in Home Space.. So i think this echo system is going to be big enough for Sony to keep PS3 for longer in the market. Sony has not abandoned it yet and i believe that the commitment they have shown to it means that they are going to go with it for reasonable time.

Reason 6. Management

Sony new management is more focussed on Software side and i think this will also impact the launch of next PS. As the new management will like to develop more applications for this machine therefore they are not going to abandon it too soon.