Just leave the city alone for 30minutes or so, seems to work for me.
I think top time it took me once to get a city (guy had 4cities, I already took 2) it took me over 3hours!! yes 3 whole hours!!! to get loyalty from 1 to 0.
In the end I didnt hit it for like 30mins (gave up) and I finally decided to scout 1 last time and found loyalty at 0 : )



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