  Context. Ultracompact X-ray binaries (UCXBs) typically consist of a white
dwarf donor and a neutron star or black hole accretor. The evolution of UCXBs
and very low mass ratio binaries in general is poorly understood. Aims. We
investigate the evolution of UCXBs in order to learn for which mass ratios and
accretor types these systems can exist, and if they do, what are their orbital
and neutron star spin periods, mass transfer rates and evolutionary timescales.
Methods. For different assumptions concerning accretion disk behavior we
calculate for which system parameters dynamical instability, thermal-viscous
disk instability or the propeller effect emerge. Results. At the onset of mass
transfer, the survival of the UCXB is determined by how efficiently the
accretor can eject matter in the case of a super-Eddington mass transfer rate.
At later times, the evolution of systems strongly depends on the binary's
capacity to return angular momentum from the disk to the orbit. We find that
this feedback mechanism most likely remains effective. In the case of steady
mass transfer, the propeller effect can stop accretion onto recycled neutron
stars completely at a sufficiently low mass transfer rate, based on energy
considerations. However, mass transfer will likely be non-steady because disk
instability allows for accretion of some of the transferred matter. Together,
the propeller effect and disk instability cause the low mass ratio UCXBs to be
visible a small fraction of the time at most, thereby explaining the lack of
observations of such systems. Conclusions. Most likely UCXBs avoid late-time
dynamically unstable mass transfer and continue to evolve as the age of the
Universe allows. This implies the existence of a large population of low mass
ratio binaries with orbital periods ~ 70 - 80 min, unless some other mechanism
has destroyed these binaries.
