Stable picosecond supercontinuum generated in long crystals is an excellent means of seeding broadband, high-energy CPA systems. The generated output energy and spectrum can be almost three times as stable as the pump for a wide range of input pulse parameters. In this work, we show this is an intrinsic property for crystals longer than the filament and for a range of input energy values. We present a description of the stability mechanism in both the visible and infrared regions together with experimental data that support the theoretical explanation.