Why do $\beta$ particles not get attracted to the nucleus?

Simply put, the electron is going too fast. The nucleus will indeed attract it and this will slow down the β particle, but this is not enough to recapture it.

To put some numbers in, beta decay energies range from a few keV to a few tens of MeV; this is much more than the few tens of eV that are typical of atomic bound states. It is only the inner shells of heavy atoms that can go into the keV regime, but those are already full so the beta cannot be captured there.

If you think about it, a beta particle is an electron (or positron) moving with high energy (which translates to high velocity due to the low mass). The coulomb attraction between the nucleons and the electron is strong, but not sufficiently strong to change the trajectory of the beta particle such that it's reabsorbed by the nucleus - it may simply change the trajectory without recapture.