The 4024 has significant output resistance, in either the high or the low state. Try replacing the "digital cap" with a cap and a 500 <a href="#">ohm</a> resistor in series, which is a rough equivalent.
Oscillation will probably stop unless you increase the feedback capacitance. The resistor severely impacts the Q of the tank circuit.
We have told you repeatedly that the 4024 outputs do not switch between short circuit and open circuit as they change states. In the low state, they connect to GND through an equivalent resistance of several hundred ohms (an N channel MOSFET). In the high state, they connect to VCC through an equivalent resistance of several hundred ohms (a P channel MOSFET). I hope you understand by now (do you?) that, to AC (RF), VCC and GND are equivalent. The capacitance change of your "digital cap" will be essentially zero as outputs change state. The series resistance will be a little different, because the 4024 does not have identical output resistance in the two output states.
EDIT: Audioguru, I was typing while you were posting.