The reason Acura recommends 91 octane for the MDX is because the engine compression ratio is 10.0:1. That's relatively high compression for a normally-aspirated engine, and high compression is a common cause for premature detonation. Lower octane fuels are more likely to experience premature detonation under high compression (i.e. knock). Your engine has knock sensors that will detect knock and try to prevent it, but to prevent knock it will retard the timing and/or change the fuel mixture/mapping as necessary. When this happens, the engine no longer performs at peak efficiency and your horsepower will suffer. Also, although knock sensors will save the engine from any longterm damage, they are meant for correcting the problem occasionally--they are not designed to prevent constant knock. So the solution is to run a higher octane, which is less prone to premature detonation.
In other words, you won't necessarily harm your engine by running 89 octane every now and then, it is not designed to operate efficiently with it constantly. To achieve the maximum horsepower available, it is recommended you run 91 octane all the time.
2005 BSM MDX w/navi