As someone that's never owned a house, that sounds like a shitty rule that should be disrupted. I'm assuming there is a positive side to that only homeowners can see.
For starters, several federal agencies actually require COA's to limit the number of units that are not owner-occupied as a condition for government-backed mortgages. Some states and local laws also place caps on this to prevent condos from being used as unregistered hotels (see eg timeshares).
As for your options? Generally, for cases like this your option would be to sell the unit or request an exemption. If you're moving far away, it's very likely that the COA will not grant the exemption, because units rented out by distant absentee landlords tend to generate the most and worst problems that COAs deal with.