Personally I am fairly certain he will not and here are a few reasons why. They are not in any order of certainty as each is a possibility.
1) Russian Investigation
Lead by the very well respected former head of the FBI, Robert Mueller, this investigation has the possibility of bringing down the Trump administration. Personally, from what I have read, there is a possibility of matters related to Trump’s business empire and its’ ties to Russian Oligarchs and possibly Russian Mafia. Those may be more problematic then possible links relating to our election, but who is to know at this point? I do believe that Mueller and team will ferret out all the issues, but it will take time.
2) Resignation-He just quits.
It is entirely possible the President just gets tired of the place. The constant haranguing of the written press and the media, plus Democrats and most recently even Republicans, may convince him it’s not worth the effort, especially when playing golf at his own resorts is a better option.
3) Base begins to erode.
If it looks like he is failing in getting done many of the things his core supporters wanted and begin to leave him in great numbers that might force a resignation, ego being what it is. The failure of healthcare may be only the start.
4) Enough R’s especially leadership says enough is enough.
So far, at least out front, they are nominally behind him in public but how long that will last is problematic. If 10 leaders descended upon the White House telling him he must go at the same time base poll numbers decline he might leave.
5) Some other reason not yet considered. This is probably the most plausible.
Those are my thoughts for what they are worth.
Best Dick g