Several reasons for this have been presented:
Firstly, sales of "traditional" (ie. desktop) consoles are showing signs of waning. The major reason for this is that (by some estimates) about 70% of video game consumers are casual gamers, and there exists nowadays a set of platforms that are somewhat of a console killer from a casual player point of view: Smartphones and touchpads. There is less incentive for casual gamers to buy the latest desktop console given that they can play casual games on their phones. This may mean that in the very near future (if not even right now) sales of desktop consoles will plummet to a fraction of what it has been in the past.
More "hardcore" gamers of course are avid console (and PC) users, and most of them don't find smartphones nor touchpads any kind of enjoyable gaming platform. The problem is that these "hardcore" gamers constitute something like 20% of all video game consumers, which is a pretty small fraction. If the trend of casual gamers moving to smartphones continues, the sales of traditional consoles may drop below what's profitable for console makers.
(This also explains why these people estimate that Nintendo will be fine, because their consoles are still in high demand by more casual gamers. They are pretty much the casual gamer brand. The Wii U was somewhat of a mistake by Nintendo, but such mistakes haven't killed Nintendo in the past either, and it's very likely that they will learn from it with their next console, and start appealing to the casual gamer masses again. Although the next Nintendo console might not be a traditional desktop console, but some kind of Wii+3DS hybrid.)
Secondly, recent consoles have sold not only because of their gaming capabilities, but also because of their multimedia capabilities. For example the PS2, the most sold console in history, was bought by quite many people almost exclusively as a cheap DVD player. Likewise many people bought the PS3 as a cheap Blu-Ray player.
However, this is changing rapidly nowadays. Multimedia in physical discs is waning out very rapidly, as fast internet connections are becoming the norm, and most multimedia services are going online. (Some video rental services have even stopped renting physical discs completely, and gone completely online.)
In other words, there is less and less motivation to buy a console to watch multimedia, as everything is being put online, and is watchable with any touchpad, PC, dedicated streaming box, or whichever machine. (I wouldn't be surprised if TV's start supporting online rental directly, without the need of a separate device.) Consoles are becoming less and less multimedia machines, and more pure gaming machines. (This can be seen in the backlash of Microsoft trying to sell their Xbox One console as a multimedia machine more than a gaming console. It just didn't work. People aren't interested in it for that reason.) And given that gamers who are interested in consoles form a small minority of the marketplace, this means that there will be less and less demand for desktop consoles.
Thirdly, Sony isn't doing all that great as a corporation. They are having some financial problems. "Sony" is not the famous high-quality brand that it used to be decades ago. Their turnover is actually becoming smaller and smaller by the year. If this trend continues, they are likely to merge with something else (perhaps even Microsoft), if not go bankrupt (although that's unlikely; a merger before bankruptcy is enormously more likely.) I do not know the actual figures, but I have the impression that Sony's PS4 branch is actually their most profitable one (with the possible exception of Sony Pictures), and given that the demand for consoles might be decreasing, as explained above...
Fourthly, while Microsoft is doing great (with turnovers that are like an order of magnitude larger than Sony's), some signs can be seen that they are slowly losing interest in the game console market. In some sense their Xbox One project felt a bit like a half-assed one, something that they did more forcefully than because it's actually a highly profitable business. (It is actually quite well known that Microsoft doesn't make much money from actual console sales. They might even lose money overall. Their profits come from game sales, Xbox Live subscription fees, etc.)
Microsoft has had this tendency in the past to try a new market, suck it dry, and then leave. It wouldn't be surprising if game consoles would eventually become another example. It is not in any way inconceivable that they will just stop making consoles after the Xbox One. (At most they might make some kind of multimedia/streaming machine which might use the "Xbox" brand name, but will be so in name only, and which might be able to play PC games, but that's it.)
Some have also speculated that a subtle change in narrative from Microsoft might be another sign that they will be phasing out their desktop console line. You see, in the past Microsoft's E3 and other gaming presentations have hyped their console exclusive games, and either not mentioned at all or mentioned only in passing that "yeah, this game will also have a PC port at some point". It has been like the fact that many of the Xbox games will also be available for the PC is kind of an embarrassing little public secret which they don't like to advertise all that much. This, however, changed quite radically in their 2015 E3 conference, where they were completely open and unashamed about their big games also being ported for the PC. It's like they aren't bothered about that at all anymore. Which might be another sign that this will be their last desktop console and they will be moving away from it in the future. (Although, admittedly, this is 100% speculation.)
This is not, in fact, far-fetched. It may be easy to think "that's just crazy; video game consoles will never die". But consider that at least 90% of game console brands have died in the past, some of which even were highly popular (such as the Sega console line). It's not inconceivable that the same will happen to one or both (or even all three) of the current console lines. If there is not enough demand, they will die, like it or not.
Note that this hypothesis is not envisioning the death of video games. They will most probably do just fine. It's envisioning the death of "traditional" desktop consoles. In a few decades such consoles might become a thing of the past in the same way as many other consumer electronics (like VCR's, CRT TV's, cassette and CD players, etc.) If the next console generation never comes, game developers might keep making games for the current ones for a decade or two, but it will eventually stop (and instead they will move to PC and whatever new gaming technology may be developed in the future).
So, in summary, the reasons why this might be the last generation of "traditional" desktop consoles are:
- About 70% of video game consumers are casual gamers, and smartphones and touchpads are console killers from their point of view. Only about 20% of consumers are actual console gamers. This may not be enough.
- Consoles used to be an affordable alternative to multimedia disc players, but the popularization of high-speed internet connections and online services are killing that market.
- Sony isn't doing all that great overall as a company. In conjunction with the above reasons, it may kill the PlayStation line.
- Microsoft is showing subtle signs of losing interest in their desktop console line. Their promotions feel a bit lackluster and forced, and their narrative has recently changed. (They used to be quite hush-hush about the fact that many of their console games were also available on the PC. They are now quite open and unashamed about it. This might mean they have a long-term plan of moving back to Windows exclusively, and abandoning the Xbox.)
- Nintendo will most probably make a 9th generation console, but it may not be a desktop console (instead being some kind of Wii+3DS hybrid.)