At present, J1819-1458 is the only rotating radio transient (RRAT) detected in X-rays. We have studied the long-term evolution of this source in the fallback disc model. The model can reproduce the period, period derivative and X-ray luminosity of J1819-1458 simultaneously in the accretion phase at ages $\sim 2 \times 10^5$ yr. We obtained reasonable model curves with a magnetic dipole field strength $B_0 \sim 5 \times 10^{11}$ G on the pole of the neutron star, which is much weaker than the field inferred from the dipole-torque formula. With this $B_0$ and the measured period, we find J1819-1458 below and close to the radio pulsar death line. Our results are not sensitive to initial period, and the source properties can be produced with a large range of disc masses. Our simulations indicate that J1819-1458 is evolving towards the properties of dim isolated neutron stars at later phases of evolution. This implies a close evolutionary link between RRATs and dim isolated neutron stars. For other RRATs with measured period derivatives and unknown X-ray luminosities, we have estimated the lower limits on the $B_0$ values in the fallback disc model. These limits allow a dipole field distribution for RRATs that could fill the $B_0$ gap between the estimated $B_0$ ranges of dim thermal isolated neutron stars and central compact objects in the same model.

6 pages, 2 figures, Accepted for publication in MNRAS