We didn't find it until 40 days after perihelion? It had already passed Earth's orbit and was quite a bit of the way out to Mars's orbital. Ugh. Can we never let this happen again?

Solar wind density is directly proportional to 1/r² (r=distance from the sun), but the speed is not a function of distance. Both are subject to significant variations related to processes on the sun's surface and in the solar corona. So you could absolutely model future anomalous acceleration in addition to what we've seen already, but the question is always how well we can resolve it, as the density will continue to drop off pretty quickly, and thus the magnitude of any pushing grows less. Maybe we have some earth-orbiting black ops imaging tech pointed up instead of down that can help us out?

Edit: There is one possible alternative explanation, but it doesn't make much sense: 'Oumuamua could be strongly magnetized, and would interact with the solar wind's magnetic field. But I dunno, if you look at 'Oumuamua's trajectory:

you'll see that the path we've gathered data for is only ~20 degrees outside of the ecliptic plane, so the solar wind magnetic field orientation might still be somewhat chaotic (reference, I will explain if prompted), which doesn't favor imparting a net force, i.e. some anomalous acceleration. But wait! This entire paragraph's worth of speculation is totally invalidated by the fact that Oumuamua is tumbling, a chaotic motion (see the intermediate axis theorem), which is guaranteed to lead to no net accrued time of some embedded magnetic field oriented in a particular direction.

Still edit: It could be possible that the object is engineered to cleverly extract energy out of electromagnetic fields like those present in a star's "solar wind".

We should send something after it. The project might take 30 years for launch and rendezvous, and then several months to send back data, but it can be done. We should look and see if we can catch it pinging somewhere else. Maybe bring a compact neutrino sensor (LOL, physics joke), 'cuz if I were an advanced species, I'd encode messages in neutrinos. It'd prevent filthy casual civilizations from detecting my interplanetary sexts (encoding information electromagnetically was so pre-post-re-evolution, circa only 2 Gyears post-Big Bang for my world, ya know?).