Can we trust the relationship between resonance poles and lifetimes?

We show that the shape resonances induced by a one dimensional well of delta functions disappear as soon as a small constant electric field is applied. In particular, in any compact subset below the positive real axis there are no resonances if the non-zero field is small enough. In contrast to the lack of convergence of the lifetimes computed from the widths of the resonances we show that the "experimental lifetimes" are continuous at zero field. The shape resonances are replaced by an infinite set of other resonances whose location and number we analyze.