how long will Polaris remain as The North Star?

It'll be a good approximation for 'north' for the next 1000 to 1200 years or so; right now, it's within 1 degree of the north celestial pole; after that, our north celestial pole will point closer to the star Alrai. 

Maybe another billion years or so. when the sun goes red giant, there will be no observers to see it.

Throughout YOUR life, so stop worrying!

The precession of Earth's axis is approximately 25,000 years and we are half way through the precession. That's the best I can do. Poor Uranus got flipped on its side and doesn't have a celestial North Star. Called True North by rocket scientists, the Stable Element does the calculations.

Answer:about 13,000 years

It will, however, eventually become our North Star in about 13,000 years. Presently, Polaris, the brightest star in Ursa Minor, appears close to the North Celestial Pole and therefore serves as our North Star.

I hope this helps you!

Polaris is nearly 3/4 of an degree from true north. So it’s not exactly the “North Star.” In about 1000 years, another bright star, Gamma Cephei, will be closer to true north.

Polaris (Alpha Ursae Minoris)

Gamma Cephei

Vega 

Deneb

Thuban 

Beta Ursae Minoris

Alpha Cephei

Iota Cephei

Kappa Draconis 

have all been pole stars. 

https://en.m.wikipedia.org/wiki/Pole_star...

26,000 ÷ 8 = 3,250 years.  Polaris is already "off" by 0.736 of a degree.

".. .Thirdly, Polaris is not exactly lined up with earth's axis of rotation. There is very low probability that any star would end up exactly lined up with earth's axis. Polaris lies at a viewing angle that is 0.736 degrees away from exact North. Because the North Star does not lie exactly on earth's rotation axis, it actually arcs through the sky every night. The arc is just so small that humans can't see it. Furthermore, earth's rotation axis is not completely fixed. Because earth is not perfectly spherical but bulges at the equator, the sun's gravitational effects on the earth are not completely symmetrical. This non-symmetry creates a very small and very slow twist on the earth that is turning earth's rotation axis away from Polaris. In about 3000 years, the star named Gamma Cephei will end up much closer to earth's rotation axis than Polaris, and will therefore be the new "North Star"...."

https://wtamu.edu/~cbaird/sq/mobile/2013/07/24/wha...

You know what you can do with that thumb down. 

Polaris will still be the north star until 

Vega takes its place in about 13,000 years. 

Due to the 26,000 year axial precession (wobble) of the Earth, 

the last time that Vega was the north star was in 12,000 B.C. 

which puts it right on target for the 15,000 A.D. timeframe.