As far as I understand weak isospin is only conserved in interactions but not as time evolves. Nevertheless, we get from Noethers theorem, because of global $SU(2)$ invariance a conserved quantity that is commonly called weak isospin (see for example this Phys.SE question).
I have never read the explicit statement that weak isospin is violated as time evolves (= during propagation), but chirality is not conserved as time evolves (see for example this Phys.SE question) and left-chiral particles carry isospin, whereas right-chiral do not. Therefore it follows from the non-conservance of chirality that isospin isn't conserved either.
How does this fit together with the result of Noether's theorem?