Period arrives late on pill

The past few months, I seem to be getting my period later each month after taking my last pill. For example, I used to always get it by Sunday morning, then it got later and was always there by bedtime Sunday, then it got later and was Monday morning etc. This month, it was late at night on Tuesday. Not only does this panic me every month, but it also means I have to start the next pack of pills just 3 days into my period.

Has anyone else experienced this?