The IC will not recharge the capacitor if its charge pin doesn't go low.

The cd4069 inverter has lots unused channels maybe they are all thats needed?

 

The BSS84 is the wrong way round in the schematic.
All unused inputs of the CD4069 should be connected to one of the power rails, or the IC will misbehave.

 

The IC supply pin and the transformer primary need decoupling caps, per the datasheet.

The IC will not recharge the capacitor if its charge pin doesn't go low.

Agreed.