No. If the persistence and standard deviation of a shock jump at the same time it means your posterior is bimodal. This can easily happen in short series because for AR1-processes the unconditional variance is given by
and it is often hard to disentangle the two parameters.
From my perspective, the trace plot is nothing to worry about. However, you should be careful in that the mean may not be a good representation of the posterior, while the median or mode may be.