The energy lost by a particle doing one turn in a circular machine is
where $E$ is the beam energy, $R$ is the bending radius, $m$ is the mass of the particle that you want to accelerate.
It comes out that for the mass of heavy particles such as muons, protons and heavy ions, the field strength of the bending magnets is still the limiting factor, but light particles such as electrons and positrons are simply radiating too much energy.
The problem is not simply wasting energy, but how to push that energy back to the beam. The acceleration is normally done in straight sections of the ring by using a radio-frequency electric field. If the field is not strong enough (in relation to the available space) to compensate the energy lost in the bending sections, the machine will never work even with an endless amount of energy available from the grid.
So you are forced to increase the radius to reduce the energy loss and have more space to compensate it, but looking at the relation above, you see that you cannot go too far. For instance TLEP plans to have a radius tree times larger than LEP, but its energy won't double the LEP one and it might be built only in view of a much more energetic proton machine coming in future in the same tunnel.
The other way is to build straight colliders such as CLIC or ILC projects, which however do not come without technical difficulties.