When kq is 0, the equation becomes 1==0, which is obviously not true, thus there is no solution for it. For that iteration, q1 is empty and you can't use indexing for it.
You can skip that value or plot a value manually for it. I have implemented the 1st option in my code below.
Note that the solve() returns the real solutions first if there are any. As the equation is a cubic polynomial in s, there will atleast be one real solution, so use the 2nd index for plotting.
syms s
figure
hold on
%Modify the loop indices to skip the value 0
for kq = setdiff(-10:10, 0)
eqnqroop = 1 + (kq*(-((4483*s^3)/5000 + (1915281*s^2)/5000000 - (551896897*s)/5000000000)/(s^4 + (52*s^3)/125 ...
+ (764541*s^2)/1000000 + (4137177603*s)/500000000 - 427810011/250000000))) == 0;
q1 = solve(eqnqroop,s);
%updated indexing
plot(real(q1(2)),imag(q1(2)),'-s','MarkerSize',5,'MarkerEdgeColor','red', 'MarkerFaceColor',[1 .6 .6])
end
