There are some weaknesses with that theory:
The signal has been detected since at least 1988. An asteroid belt around a sun would be dynamic and continuously changing, making it unlikely for the same 20-minute repeating pattern to persist for decades.
The bursts vary in intensity and duration, and occasionally don't happen at all within a given window. This is not consistent with a simple periodicity expected from gaps in an asteroid belt.
The repetition period of 22 minutes is very slow for an asteroid belt around a sun. Typical asteroid belts have orbital periods measured in hours to days, not minutes.
For asteroids to completely block the emission from the sun during each 20-minute gap would require an extremely large number of asteroids, far more than seen in our own solar system's asteroid belt.
The semi-randomness of the signal is difficult to explain by gaps in an asteroid belt, which would be expected to produce much more regular periodicity.
The required size and stability of such an asteroid belt, persisting for decades around a sun, is not consistent with current astrophysical models of asteroid belt dynamics.
Here are some other theories that could potentially explain GPM J1839–10:
Precessing black hole - The repeating radio bursts could be caused by a precessing black hole accreting material. The precession period of around 22 minutes could explain the observed repeating pattern. However, such slow precession is not well understood for black holes.
Colliding neutron stars - GPM J1839–10 could be two neutron stars in a binary system that collide every 22 minutes, producing the radio bursts. However, the persistence of the signal for decades is difficult to explain in this scenario.
Magnetar with fluctuating magnetosphere - A magnetar, a type of neutron star with an extremely powerful magnetic field, could have a magnetosphere that fluctuates on a timescale of around 22 minutes. This could cause repeated emitting and blocking of radio waves, producing the observed pattern. However, current magnetar models do not predict such slow fluctuations.
Interacting binary system - GPM J1839–10 could be two orbiting objects that interact every 22 minutes, disrupting material and producing the radio emission. Possibilities include a neutron star and black hole or two neutron stars. However, the required orbital period of around 22 minutes is extremely wide for a compact binary system.
Strange state of quantum chromodynamics - Some theorists have proposed exotic states of matter governed by quantum chromodynamics that could provide a source of persistent but fluctuating radio emission. However, such proposals are highly speculative at this point.