State Variable Filter - Unexpected High Frequency Behavior
The shown problems at higher frequencies are typical for all inverting opamp applications. Here, the last stage is an inverting integrator circuit with capacitive feedback.

What happens as a result of high frequencies at the input of the last stage?
There are 3 major effects: 

(a) The open-loop gain of the opamp drops continuously so that the circuit cannot work properly anymore,

(b) the impedance of the feedback element (capacitor) is reduced continuously and 

(c) there is, therefore, a rising part of the input signal that arrives at the output node using a "wrong" way: Directly through the capacitor. This current, which is NOT driven by the amplifiers output node, causes a rising output voltage across the finite output resistance of the opamp. It is even worse, because this finite output resistance is not constant but goes high with rising frequencies.

As a result, the ouput signal goes high with the frequency because of this unwanted effect (parasitic portion of the input arrives the output node with an even increasing characteristic).