Short answer
In case of Pacinian corpusles, the adaptation is generally ascribed to the mechanical characteristics of the outer capsule of the receptor. The capsule's onion-like structure quickly molds itself to pressure stimuli, thereby rapidly desensitizing the receptor.
Background
There are two classes of mechanoreceptors in the skin based on their rates of adaptation, namely rapidly adapting and slowly adapting receptors. The Pacinian corpuscles (and hair follicle receptors) are of the rapidly adapting type. These receptors swiftly become unresponsive (they adapt) when a pressure stimulus is applied, but faithfully transmit rapidly changing stimuli (such as vibrations).
Pacinian corpuscles are specialized vibration receptors. Their dendritic region is shaped as an onion-like structure with layers of stacked lamellae:

Specialized dendritic capsule of the Pacinian corpuscle. Source: Biologymad
These lamellae act as high-pass filters that result in a sharp drop in sensitivity below 150 Hz (Johnson, 2001). If this capsule is dissected from the receptor and a pressure stimulus is directly applied to the sensor element underneat the capsule, the receptor response to a sustained stimulus substantially increases (Mendelson & Loewenstein, 1964). Basically, these elastic lamellae mold their shape to the stimulus and pressure stimuli are only transmitted for a few milliseconds, after which the lamellae absorb the pressure. So only a one or a few spikes are generated at the start of a pressure stimulus. Upon release of the pressure stimulus another spike or two are generated. Hence, a continued pressure stimulus is not faithfully reproduced. However, vibratory stimuli generate spikes on the pressure onset as well as offset as well, and this happens on every phase of the vibration. Hence, vibratory stimuli are faithfully transmitted.

Response of Pacinian corpuscle to a sustained pressure stimulus (indentation of the skin) and superimposed vibratory stimuli. Note the vigorous response to vibrations, but the rapid adaptation to the static pressure stimulus. Source: Zavantag
Although the adaptation of the Pacinian corpuscle is generally ascribed to the mechanical properties of its capsule, further high-pass filtering may be accommodated by neurophysiological properties that limit spike initiation, as described by Cagliari2005.
References
- Johnson, Curr Opin Neuobiol 2001;11:455–461
- Mendelson & Loewenstein, Science 1964;3618:554-5
Further reading
Why are skin tactile receptors considered to be phasic receptors?