Neutral, circumpulsar debris that enters the magnetospheres of neutron stars can disrupt current flows and electromagnetic radiation and thereby account for some of the intermittency seen in radio pulsars. This paper considers asteroids that form from supernova fallback material and how they migrate into the pulsar light cylinder before evaporating, ionizing, and perturbing particle acceleration regions. Such intrusion is expected primarily for pulsars with long spin periods and relatively cool surfaces. We show that debris disks undetectable either directly or through reflex of the neutron star can provide sufficient material over the radio-emitting lifetime of a pulsar to account for nulling and burst phenomena that occur on timescales of seconds to months. The quasi-periodic bursts in B1931+24 may be driven by a large orbiting object that perturbs a debris disk episodically.