In order to oscillate, the loop gain of the circuit has to be greater than 1 at the oscillating frequency. That is to say the gain produced by the amplifier has to be greater than the in-phase loss in the feedback path. If the loop gain is >1 then the signal will get stronger each time it goes around the loop, but if it is <1 then any oscillation will get weaker and die out. So the reason your 90kHz circuit doesn't oscillate is that its loop gain is less than 1.
But if it worked at 1kHZ, why does it not work at 90kHz? Because when you changed the component values to increase the frequency, you also lowered the loop gain. If you changed the values proportionally then the feedback loss should not have changed, so it must have somehow lowered the amplifier's gain. To understand how this may have happened you have to know what determines the gain of a transistor amplifier. Here's your amplifier with the feedback load represented by C1 and R1:-
simulate this circuit – Schematic created using CircuitLab
A bipolar transistor is a current amplifier. In Common Emitter configuration the Base I/V characteristics are similar to a diode, and the Collector sinks a current which is relatively insensitive to Collector voltage. In practice this means that the transistor acts like a voltage controlled current generator, and its voltage gain is proportional to the Collector load impedance. With a Collector load of 1K this circuit has a voltage gain of about 300 (49.5dB).
However any external load impedance will be effectively in parallel with R6 and so will reduce the gain. At high frequencies C1 is a virtual short circuit, so R1 is in parallel with R6 which reduces voltage gain by about 10 times to 30 (29.5dB). Will this lesser gain be enough?
With the feedback component values shown in your circuit (R1-3 = 100Ω, C1 = 470nF, C3-4 = 100nF) LTspice says the oscillation frequency is 4.9kHz. At this frequency the filter has a loss of ~20dB. Since the total loop gain (29.5dB-20dB = 9.5dB or 3) is greater than 1 the circuit should oscillate. However with such low gain LTspice thinks it will take about 5ms for the oscillation to build up to full strength.
Now what happens when you try to increase the frequency? If you reduce the values of R1-3 then their lower impedance will cause amplifier gain to be further reduced, perhaps dropping loop gain below 1 and preventing the circuit from oscillating. If you only reduce the capacitor values then the impedance at the oscillating frequency should stay the same, so provided the transistor still has sufficient gain at the higher frequency it should work.
To get 90kHz in LTspice I changed C1 to 26nF and C2-4 to 5.5nF. Changing all the capacitors by equal proportions should ensure that the loss remains constant. However In a circuit like this which has marginal gain, many factors can affect its ability to oscillate. Increased load on the output, a transistor with slightly lower gain, parasitic capacitance, a different bias point or lower supply voltage, even capacitor and resistor tolerances could be enough to stop it from working.
To get stronger and more reliable oscillation you could increase the values of R1-R2 to reduce loading, and make C1 closer in value to C2-4 to increase its contribution to phase shift and reduce loss at the oscillating frequency. The ultimate limit on frequency may be when the capacitors are so small that parasitic capacitance takes over.