The issue that caused this problem is related to the driving capability of the input signal and the setup of the filter. The MAX11046 has an internal 15pF sampling capacitor, which needs to be charged every time a measurement is taken. If the internal sampling duration is too short, and the signal is converted before it has completely been built on the sampling capacitor, this issue will occur.
To resolve this issue, the signal's driving capability needs be increased, by either decreasing the serial resistance or applying buffers.