Region of root locus not inside the feasible region for a given performance specification
The root locus will start at the open loop poles and move toward the open loop zeros as the gain is varied. Your pole cannot get past the zero that is located in the yellow region. This pole that is close to the imaginary axis will be dominant, meaning it will dominate your response times, slowing down the entire system. One approach is to cancel that zero with an additional open loop pole at it's location, unless that zero was introduced by your controller in which you have the ability to move it to be out in the white area, or eliminate it entirely.
It appears that the zero that terminates the closed loop pole as shown is due to $(s+A)$ in the numerator, in which case choosing a value for A that is within the white region should allow the pole to extend further to that point as the gain is increased. Also, the pole and zero due to the Pade approximation does not appear to be visible in the root locus.
To see how poles close to the imaginary axis are dominant, consider the simple case of $x(t) = e^{-at}$ which has a Laplace Transform $X(s)=\frac{1}{s+a}$  (which is a pole at $s= -a$. The time domain equation is a decaying exponential with time constant $a$, if a is very small this will take a very long time to decay. If $a$ is very large, the decay rate will be very fast.