It is more related to the needed strength of the magnets to keep the particles on track and also the synchrotron radiation. The first issue is that the lower the radius of the circle, the stronger magnetic field is needed because of the increased centrifugal forces. The second issue is that synchrotron radiation leads to loss of energy. It is again proportional to the acceleration perpendicular to the vector of the velocity of the particle [0].

[0] https://en.wikipedia.org/wiki/Synchrotron_radiation