  We examine the influence of probe laser intensity fluctuations on
hyper-Ramsey spectroscopy. We assume, as is appropriate for relevant cases of
interest, that the probe laser intensity $I$ determines both the Rabi frequency
$(\propto\sqrt{I})$ and the frequency shift to the atomic transition $(\propto
I)$ during probe laser interactions with the atom. The spectroscopic signal
depends on these two quantities that co-vary with fluctuations in the probe
laser intensity. Introducing a simple model for the fluctuations, we find that
the signature robustness of the hyper-Ramsey method can be compromised. Taking
the Yb$^+$ electric octupole clock transition as an example, we quantify the
clock error under different levels of probe laser intensity fluctuations.
