As others have said, if Xbox remains profitable then they'll stay, if it doesn't remain profitable....not sure. Sure, MS stuck out with the original Xbox, but given its main job was to establish the brand and get a foothold in the market, investors were prepared to wear the multi-billion dollar losses. X360 was overall profitable and much more successful for them and so investors were happy, but if (and thats a big if) Xbone is unprofitable for an extended period (say 2 years) then MS may experience growing pressure from investors to spin it off.

Investors want return on investment. They started to get that return on investment during the 360 days, but if that goes the other way with Xbone then they may pressure MS to cash out of the business, especially if the industry starts to decline. Not saying MS should, but the herd mentality of investors is all about short term gain, not long term growth.

What a triky statement. Indeed, if they are making profits they wont leave. But, if they have to cut the price of the console to stay competitive they will take losses. What now?

Personally, i would think it would benefit everyone if they did leave. They could focus on their more profitable businesses, Sony wouldnt be so hard pressed to take such insane financial risks, Nintendo might get a big enough pie of the home console market and the consumers would be freed from all the gouging that microsoft tries to do ontheir wallets.

Seriously speaking though. This is a business microsoft cant win. They will always be running for a tie at best. Do all those losses make sense for such a limited reward?

As long as they are making a decent return they wont leave.

With the new leadership possibly being less invested in what was predominantly Ballmer's vision, I could see them being less dedicated to the division as a whole, although if the Xbox program as a whole keeps bringing in money, i don't see a reason to kill it, especially as those resources would not be easily transferrable to other endeavors.

Basically, if the Xbox is lossmaking for any number of years in this generation, i could see them dropping it. Microsoft is not going to play around with a money-loser anymore, even if they can afford it, due to possibly being less important to their division.

Um, no of course they won't. But the X1's failure will make shareholders put more pressure on MS to get rid of it.

heres the problem 2 major investors are already asking to get out of xbox , if it doesnt make money this gen they have more leverage and may have more support to get them out.

They haven't left the mobile market despite Windows Mobile not getting a large market share.

They bought Nokia. Maybe they'll buy SCE if the rest of Sony isn't doing well. ;)

Btw, making a profit is not the only thing to look at.  Companies have different profit expectations, for example consumer electronics business like Sony target ~5% profit whereas tech companies like MS target much higher profit.  If they have a segment earning only 5% or less it's not good for their investor's expectations and can negatively affect their stock.

P.S.3 was selling more than 360 with a higher price tag,

P.S.4 is selling more than Xbox1 due to it being a better console aswell as being cheaper

even if same price P.S.4 will sell more

Microsoft is a business.
Microsoft is a business with shareholders.

Shareholders don't care what consumers want or think, they want ever-increasing profits.

If the Xbox One proves to be unprofitable, there is indeed a high probability it would get closed down/sold/spun off in order to appease the shareholders.
The same goes for Sony and Nintendo too.

This is why I have always been against any singular console taking majority stake of the console market, it is bad for everyone, reduces competition which then in turn stagnates innovation and potentially increases prices.