The answer to my question is: the Maximum Frequency does not dip, even though the Resource Monitor indicates it does.
My process was running at Real-Time Priority, while the Resource Monitor was running at Normal Priority. As soon as my process got really busy, the Resource Monitor was not granted the CPU cycles required to measure the values it was monitoring. As a "consequence", it erroneously displayed zero values.
One thing that surprises me in particular is the fact that the GUI of the Resource Monitor was happily updating, the graph shifted leftwards without any noticeable irregularities. The cause would have been much easier to identify if the GUI would have stalled as well.
Sorry for answering my own question -- not sure whether this is an appropriate thing to do. I do not want other people to spend time on this in vain either though.