tl;dr: It's a hard problem. While this answer says
However, space is big "therefore ʻOumuamua will never return".
I say never say never!
What natural mechanisms could lead to the unlikely case of the same rogue asteroid or planet passing through our solar system twice?
I can think of three mechanisms.
1. Stellar and solar-system pinball
Under normal situations an asteroid or planet could not swing around a massive object, make a U-turn, and come straight back nearly along it's same path after a 180° deflection. However deflections by two or more large bodies can do it. Those two bodies could be
- Two unrelated stars: This would make a triangular path; Sun, star-1, star-2, Sun again.
- A double star: Three-body unbound orbits are crazy and chaotic and just about anything can happen including a 180°U-turn. This is my favorite since it only requires one encounter and star systems of two or higher are pretty common.
- A star and its planet: Stars with Jupiter-size (and larger) planets are pretty common, and a hyperbolic orbit around a star doing much/most of the bend with the planet doing the rest of the 180°U-turn is possible.
- other variations on this theme.
2. General Relativity (or Neutron Stars)
A black hole: As explained in answer(s) to Could a trajectory around a large mass ever deflect by more than 180 degrees due to general relativistic effects? "...there is no limit on how many "laps" a hyperbolic orbit can make before it returns to infinity." That's in the limiting case of a zero-mass object. For large mass ratios such as an asteroid or planet versus a black hole, the maxiumum number of turns an unbound orbit can make is about 0.41 times the mass ratio, which would be greater than a million for an Earth-sized planet and a vanilla stellar-collapse black hole.
A neutron star: I am not certain yet if the GR effects due to a neutron star are strong enough to produce a 180°U-turn without a destructively close approach; I'm currently working on this...
3. Galactic roller-coaster
The solar system orbits the galactic center at about 220 km/s with a period of about 250 million years. That speed is an order of magnitude or possibly two faster than the orbital speeds of asteroids and planets within solar systems. Jupiter orbits at 13 km/s and (486958) 2014 MU69 (Ultima Thule) moves at 4.6 km/s. So no mater which direction our rogue friend leaves the solar system, it's going to be moving around the galactic center with a nearly parallel orbit to that of the solar system, and it's going to be doing a complicated dance above and below the galactic plane as our solar system is doing, due to the restoring force of the galactic disks's gravity. This can bring us and our rogue friend back together in a way that would at first surprise us both until we remember how stars move in the disk.
For all of these the probability is small, but the single collision options (double stars, solar systems, black holes, neutron stars) may make the probability better than the two unrelated star sequential scattering scenarios, and the galactic plane oscillations don't require a near approach to any other body at all.
So I think the statement:
...Therefore it will never return.
could be considered cavalier and possibly scientifically unsupported.
It's a hard problem, so never say never!