Hi,
You have one parameter for each observation. When one observation is removed, the posterior for the corresponding parameter changes a lot and importance sampling is not able to handle this. This can happen also when the model is correctly specified. See a similar example in Roaches cross-validation demo. In this case you can use quadrature integration to integrate over that one parameter as shown in the integrated LOO section of the same demo.
btw. the information from that thread and more has been collected to CV-FAQ and loo package glossary.
Not related to your main question, but it’s not the model that converges, but MCMC (or at least the diagnostics don’t indicate MCMC convergence problems, which is not yet a guarantee of sufficient convergence).