Maybe the overshoot is taking so long, greater than the windowsize?,
Quite possible, (no expert disclaimer still applies 
if overshoot is too large it can take quite some time to get at the setpoint, depends on the system - materials, physical properties etc.
Note there are systems in which overshoot is not an option. E.g. consider an system that heats biological samples for analysis. If the samples become too hot the proteins can get disrupted.