Carola Binder has a post up that looks at a working paper [pdf] by Michael Ehrmann from the Bank of Canada. The result he found is that inflation expectations depend more on lagged (past) inflation than expected (future/target) inflation when inflation is below target than they do when inflation is above target.
Although it is presented in an expectations-based model, the result is pretty clear: if inflation is below your target, it is more likely to stay below your target than rise up to it.
This is exactly what the information transfer model says -- once the maximum possible inflation rate (a steadily decreasing function of the size of the economy) falls below your target, observed inflation will tend to come in below target (until there is monetary regime change). There is no symmetrical problem if inflation is above target.