Time constrained loop unit

I have a particularly difficult loop, in that it consists of two variables looping and sowing the result if a criteria is met. Overall it works for me, but some certain values for my variables take extremely long to compute, whilst most others go through instantly.

I would thus like to apply a time constraint for every calculation in my loop, but instead of aborting, i'd like for the loop to just break and continue to the next iteration.

How would i do this if my code looks like so:

Reap[Do[Do[(g = i;
o = 1;
Kbt = 1;
a = j;
p := Solve[(s^2) + g*(s^a) + (o^2) == 0, s];
b = Abs[Re[s /. p[]]];
ot = Abs[Im[s /. p[]]];
fi = Pi + ArcTan[(-1)*(ot/b)];
v = 2 ot - ((g*a*Sin[(1 - a)*fi])/((b^2) + (ot^2))^((1 - a)/2));
u = -2 b + ((g*a*Cos[(1 - a)*fi])/((b^2) + (ot^2))^((1 - a)/2));
Om = ArcTan[u/v];
B[r_] := (a big function);
H[t_] := (a big function);
fm = FindMinValue[H[t], {t, 1, 10}]);
If[fm >= 0, Sow[{a , g}]; Break[]], {i, 0, 5, 0.01}], {j, 0.44,
0.98, 0.01}]]

This code gives me a load of points which i want to graph (the criteria for each point is that it is positive in the interval 1-10, which i determine with FindMinValue on said interval). However having it take days because of some points that could easily be replaced with the next iteration or previous one, is a tad tedious.