The circuit probably uses a marconi oscillator, the simplest likely cause would be the HF being lost in the weld cables or torch assy, have you checked them?
Theres also usually a HF coupling transformer that couples the HF into the weld current output, it could be flashing over, then theres the resonant caps in parallel with the HF transformer primary, one or more could be leaky worsening when hot.
If the spark gap flashes over theres not a lot more to check than this I can think of, can you borrow another torch to try?