Protect ADC - Input HF
Consider common mode and differential mode impedances. (Zcm, Zdm)

Consider EM coupling impedances from stray sources, which depends on layout geometry.

Determine the spectrum of the burst with Spectrum Analyzer or DSO with suitable method such as in situ stripline proper impedance matched -10dB directional couplers.

In order to improve CMRR of an unbalanced line, you need a differential input or a BALUN rated over those frequencies. A Balun raises Zcm while maintaining Zdm to improve CMRR of stray noise. This can be a hybrid Txfm or a ferrite bead with both sig+gnd passed thru.with n turns using AWG 30-36 magnet wire similar to a 3dB splitter materials.

See if this helps you prevent the burst and verify it.

I trust you are using semi-rigid copper cable thruout, with high quality connectors.