your confusing 3D polygons with 3D depth

Why?  The PSP is hugely successful for a non-Nintendo portable system.

Practical reasons mostly surrounding how even the PSP used the razorblade method, Sony took a hit, then made it up later, putting their company back in the red when they've just started to hit the black after losing 3 billion dollars is not what Sony HQ nor investors want to hear, if it comes it'll be a while.

3D depth in 2D games isn't exactly the most essential of things. And it can easily become cheesy.

I believe information has already crept onto the internet that Sony is working on a successor to the PSP.  I'm sure it won't be out until quite some time after the 3DS, though. 

Uh rumors about Sony working on a new PSP have circled for 3 years and still nothing, most if not all are false, some of the more recent ones sound promising, but still a bit of a stretch.  If the more recent rumors are true it will be radically different than the PSP we have now, and likely not even similar types of games, since the latest rumor is the PSP2 will be a gaming cellphone, meaning digital download for all your games on 3G... likely <1GB... which means more simplistic games on the visual and content levels.

I also heard of the rumor of the PSP2 being a kind of gaming cell phone, but read an article pointing out several logical holes in it.  For instance, a PSP-phone would likely be a weaker overall system to the PSP and that such a project is very much not the way Sony does business.  On top of which, Playstation is a very strong brand--they're not going to muddle it with a cell phone--for one thing, look at the current PSP commercials, which openly mock cell phone gaming.  The PSP-Go has also not been met with much success, owing to the idea that Sony will likely still focus on a physical-media-based system the next time.  Frankly, I wouldn't be surprised to see them using "shrunk" Blu-Ray technology in order to maintain the same basic game shape as the current UMD's, but with a micro Blu-Ray-based disk inside the UMD shell.  This, if you think about it, would be the smart way to go because it would allow the system to be backwards compatible to the original PSP. 

I have no doubt at all that a new Playstation-branded portable device is in the works.  Sony may be waiting right now to see how the 3DS looks on a technical level so they can attempt to one-up the thing.  Who knows?  Sony may be working right now to secure rights to make the successor to the PSP also feature a built-in 3D screen.  They copied the Wiimote, after all.

But, frankly, with 40 million in sales, the PSP is a resounding success.  That's still higher numbers than a lot of otherwise successful game systems--such as the original Xbox or the Sega Game Gear (which managed only around 9 or 10 million).  Sony's not just going to give up on their portable system.  They have a ready fanbase, after all.

Never said they would nor does anyone think its a failure by any means... but they're really not in the position to stay on their old model of making expensive tech and selling it at a loss to make money later, it just doesn't work from a business standpoint for them unless they want their investors to go batshit crazy which is almost what happened after the PS3 launch, once a business model has been shown to have cracks it makes investors gunshy, who wants to invest in a company that might be ready to lose millions more, and with the restructuring of the company as a whole I just don't see HQ letting that happen.

To be fair, while I'm sure some investors took some issue with the PS3's launch, it's never-the-less been successful from a giant company that is typically pretty successful.  I doubt the PSP lost all that much money, especially considering it's resounding success.  I know if I were a long-time investor of a company with Sony's track record, I might take some of the PS3 issues with a grain of salt. 

I personally question the idea of developing and expensive system and selling it below cost with the goal of making up losses on game revenue, and I always have.  But, that formula was hugely successful with the PS1, PS2, most likely with the PSP, and eventually with the PS3.  The PS3 launch--and it's first year--was certainly messy, but the system has still been successful. 

Sony clearly isn't interested in developing cheap tech to sell affordably.  They've always been big on quality and high-tech over affordability and low-tech.  Granted, it cost them the home video market when Sony's technically superior Beta format lost to the cheaper VHS, and the PS3 initially stumbled in the face of the Wii and Xbox360, but the gamble has certainly paid off most of the time--which is one of the reasons Sony is the gigantic company that they are.

I forgot, the last rumor I heard of the PSP was that Sony had developed a core that is roughly half the power of the PS3--but the same general tech.    A smaller Cell processor.  If true, that's damn impressive.  Where the hell did I read that...?

Anyway, Playstation is one of Sony's biggest brands.  I'm sure Sony will still give that division some ample freedom for development and marketing.

Uh... you do know how much the PS3 lost them right?  It caused a lot of fuss with investors, since the damn thing lost them over 3 billion dollars wiping out all the profits of the PS2 era (including the PSP) and eating into what they made on the PS1, which was the last figures I got my hands on over a year ago and since then SCE has only had one quarter of profit... in all likelihood they lost what they gained off the PS1 as well.

As for advancing tech.... PS1 was far from being the best tech, CDs had been used in the past, and the hardware was weaker than that of its direct competitor, PS2 was lacking as well but at least was the first to start using DVDs... PS3 has been their first console that has really pushed bounds, but it much like the PS2 is a bit convoluted to develop on with strange architecture, over time they've started to figure out how to get the juice out of the machine but when the thing first came out even their own menu system wasn't very well optimized and if they hadn't fixed it Uncharted 2 wouldn't look as good as it does. 

PSP was sold for a loss that you can see as a direct impact on their profits the first couple of years, if they do that again with the PSP2, they don't have a PS2 that will keep the company in the black.

PS3 making up for it's losses is almost impossible, it had 4 straight years of losses and just last quarter they finally hit that mark they needed, but Sony has had to sacrifice their share of format royalties on PS3 just like they did on PSP so it would encourage more third party support, they wont have that royalty revenue like the PS2 era... which the PS2 didn't even make them 3 billion dollars what hopes does the PS3 have?