oscillator design with a comparator
Two remarks:
1. The HC14 oscillator in general should better use a single gate than three cascaded (cause the part is already buffered internally, you're effectively chaining 9 inverters!), but probably that isn't the issue here.
2. The issue most likely is susceptibility for interferences from the enviroment, mainly low frequency AC voltage, but may be also strong RF fields. For an open capacitor, this problem is by design. You can't remove the interference, you can try to suppress the influence by an appropiate postprocessing of measured frequency.
A more sophisticated circuit could utilize parallel resonance with an inductor at the input to suppress low frequency coupling.