AD9514 Low Frequency De-sync

We are having problems that seem related to a previous question that never appeared to be fully answered:

In our case we're seeing it with a AD9102-EBZ. Our application requires a 4kHz operating frequency and we are attempting to replicate that on the development board. However, once the input frequency starts approaching 3.6MHz, the system began to act sporadically. We've isolated the problem to the on-board AD9514 by putting a scope probe on the AUX_CLK input. As the output frequency approaches 450kHz (which would equate to a 3.6MHz input with the default divide by 8 in the AD9514) the AUX_CLK input begins to drop out of phase and act sporadically.

We could change the divider to the max of 32, but unless there's another element I'm missing we would still be far away from the 4kHz target that we were hoping to test. For the time being we've been using a target frequency of 4MHz (which would be a 32MHz input) for development for now and the system has been working well. We could try to remove the AD9514 entirely from the equation but we would prefer to only do so as a last resort.

The solutions offered in the linked question appear to only focus on the AD9106 operation, however in this case we can see that our issues are not with the device under test but rather the AD9514, so none of those solutions would help.

Our question is: Is there a minimum frequency requirement for the AD9514? If not, why would the setup as defined in the AD9102-EBZ's schematic have such poor operation?