Manganese is like bricks in a wall, and zinc is a guest that comes and squeezes in between them. If the guest sits awkwardly, it pushes a brick out of the masonry. That's roughly what happens in a zinc-ion battery: during discharge, zinc ions insert into the crystal lattice of manganese oxide, and manganese starts to wash out into the solution.
Scientists calculated how energetically favorable it is for manganese to leave its site and found that in the discharged phase (ZnMn$_2$O$_4$), this happens easily. The reason is the awkward, distorted coordination of zinc, which weakens the bonds between manganese and oxygen. Nuclear magnetic resonance experiments performed right while the battery was operating confirmed that manganese leaves for the solution throughout discharge, and partially redeposits on the electrode during charging.
This discovery explains why zinc-ion batteries still can't compete with lithium-ion ones in longevity. Understanding the mechanism suggests how to tweak the cathode's composition or structure so that zinc sits more comfortably and doesn't push out manganese. Then cheap and safe zinc batteries could store energy for entire neighborhoods.
Manganese dissolved in the electrolyte can redeposit on the electrode during charging, the battery partially heals itself, but not completely.
In the movie The Matrix, humans are used as batteries, but their bodies aren't designed for that, just like the manganese cathode, which degrades from improper ion seating.