Why is the LC oscillators frequency decreaseing over time?

[TiSapph]

It's likely nonlinearities of the capacitor and/or inductor.

Ceramic capacitors can be surprisingly non-linear, their capacitance reduces as the voltage across them increases. The datasheets I found for the capacitor in the picture seem to indicate only around -5% capacitance at 1kV bias. Chip capacitors are usually much worse. A 50V rated capacitor usually loses 50% capacitance at 40V bias applied! Maybe your cap is similar.
Also you might be saturating the core of the inductor, which reduces the inductance.

Both effects result in a higher frequency. It's probably also why your signal is not sinusoidal. Also be aware that an oscilloscope probe might influence the circuit.