Image 1 Caption: A cartoon of a near-Earth asteroid (NEA) on a apsidally precessing orbit in the inner Solar System.

NEAs are defined as asteroid with perihelion ≤ 1.3 AU. This usually means the asteroid comes within the perihelion of Mars 1.38117 AU (NASA: Mars Fact Sheet).

Where do NEAs come from?

1. Astronomical perturbations (mostly gravitational perturbations) create NEAs and then can turn them into PHAs.

2. NEAs must mostly originate as asteroids in the asteroid belt or some Trojan zone or are extinct comets trapped in the inner Solar System (radius ≅ 5.2 AU: i.e., ∼ mean orbital of Jupiter) where they are asteroids at least for NEA purposes.

   In the asteroid belt or Trojan zones, the orbits of asteroids are stable.

3. For the asteroid origin, a Jupiter astronomical perturbation or an astronomical perturbation by another asteroid (which often is a natural gravitational assist AKA gravitational slingshot maneuver)) or a fragmenting collision of asteroids sends an asteroid (which could be a fragment asteroid) into a sufficiently near-Earth orbit in the inner inner Solar System that it becomes a NEA.

1. Astronomical perturbations (mostly gravitational perturbations) will eventually cause it to impact a large inner Solar System object (Sun ☉ (maybe ∼1/3 of the NEAs), Mercury ☿, Venus ♀, Earth ⊕, Moon ☽, Mars ♂) or be ejected (often by what can be called natural gravitational assists) out of the inner inner Solar System.

2. To be a bit more precise, the motion of a NEA is often an apsidally precessing orbit due to Jupiter's gravity.

   The Image 1 above and Image 2 below illustrate apsidally precession.

   The apsidally precession makes probable a strong interaction with an astro-body of the an inner inner Solar System (Se-560) and can turn NEAs into PHAs.

   Note apsidal precession is NOT the same as axial precession. But both processes are usually just referred to as "precession".

   

3. NEAs typically have lifetimes of only a few million years (see Wikipedia: Near-Earth object: Near-Earth asteroids (NEAs)).

   Because they last so little time compared to the Solar System age = 4.56730(16) Gyr BP (set by first solids formed in presolar nebula)), NEAs must be replenished by the processes described above.

Images:

1. Credit/Permission: © David Jeffery, 2003 / Own work.
   Image link: Itself.
   
2. Credit/Permission: © UserWillowW, 2008 / Creative Commons CC BY-SA 3.0.
   Image link: Wikipedia: File:Precessing Kepler orbit 280frames e0.6 smaller.gif.