Based on the reference cited in the question comments, this particular situation occurs when you implement a controller designed in the continuous time domain on a discrete time system with measurement or model uncertainties.
Designing the controller in continuous time means that the sample rate is not taken into account/is assumed to be infinitely fast. Therefore the controller can behave very differently for different sample rates, even if the control gains remain unchanged. In particular, increasing the sample rate can destabilize the system by making it more sensitive to noise/uncertainty in the measurements (especially with PD and PID controllers).
A simplified example
You have a proportional-derivative controller, with a derivative gain $K_d = 1$ (the proportional part is not really important for this example). Your control system has a sensor which gives you a measurement of your error with a random uncertainty up to $w = 0.1$ units. At a certain moment in time the true error signal is changing at a constant rate of $\frac{de}{dt} = 10$ units/s.
First you implement your controller with a sample time of $T=0.1$ s. You estimate the current rate of change using a first order approximation, and it just so happens that you experience the maximum error in this timestep:
$\frac{de}{dt}_{measured} = \frac{e(k)-e(k-1)}{T} = \frac{\frac{de}{dt}T + w}{T} = \frac{de}{dt} + \frac{w}{T} = 10 + \frac{0.1}{0.1} = 11$ units/s
Therefore the output of the derivative part of your controller is $11K_d=11$, i.e. 10% higher than the ideal output of the continuous controller ($10K_d=10$). Notice that the contribution of the error term to your controller output is inversely proportional to sample time, therefore smaller sample times (faster sample rates) increase its effect.
Then you decide, faster must be better, so you decrease the sample time to $T=0.01$ s. Now, in the same situation, the estimated rate of change of error is:
$\frac{de}{dt}_{measured} = 10 + \frac{0.1}{0.01} = 20$ units/s
The output of the derivative part of the controller is now $20K_d = 20$ i.e. almost double what it was before, and 100% higher than the ideal output. Your controller is now behaving more aggressively even though the true rate of change of error has not increased.
The problem is exaggerated in this example by using a first-order approximation, but more complex approximations of the derivative will only mitigate, not eliminate, the problem. The fact is that changing the sample rate of the system can have a negative impact in the presence of any kind of measurement uncertainty. Now, whether your controller performs better or worse when you increase your sample rate depends on the relative magnitude of the uncertainty versus the rate of change of the error signal, the relative magnitudes of your derivative and proportional gains, and the type of approximation you use for your derivatives.
Conclusion
If you are designing a system where the controller cannot be approximated as continuous and there are measurement or other uncertainties present, increasing the sample rate will not necessarily increase performance because the influence of the uncertainty on the control input will increase.