Synchrotron radiation takes energy from an accelerator beam and is related to acceleration. Why would you expect the problem to be more severe for electron accelerators than proton accelerators?
Synchrotron radiations are produced when charged particle is accelerated radially. The force applied by the synchrotron is constant and therefore the acceleration of less massive particle will be greater.
The radiation is produced when the beam of particle travels in a curved path. The mass of electron is much less than mass of proton thus when electron is accelerated in a synchrotron the amount of synchrotron radiation produced is much higher.
Thus synchrotron radiation takes more energy in case of electron acceleration in a synchrotron.