That's interesting, that harmless looking transfer function really seems to be problematic for Matlab.
You have already noted that the root locus your are getting is certainly wrong -- it is not symmetric wrt the real axis, and also the real axis left of the pole at -1.3 has to lie on the root locus entirely.
Two solutions I can offer:
- As Azzi has suggested, supply a vector of gain values with higher resolution, I suggest
- Instead of drawing the root locus and eyeballing it, do some math to find the imaginary-axis crossings. The Routh-Array and Hurwitz Criteria are favorites here.