The ability of an "S" gate to source current depends on the voltage. The 2 mA spec is at a voltage of maybe 0.5V. As the voltage at the gate input rises the source current is reduced. At a voltage of 1.6 volts the source current from the "S" input is reduced to a level where 1.6 V across the 33KΩ resistor is no longer sufficient to allow the capacitor to continue to discharge below 1.6V. This would not depend on the ability of the signal generator to sink current.