why is it that the fan belt keeps splitting in two and falling off.

Misalignment exist within the drive belt 'pulley system' .. If it's not conspicuous using conventional methods i.e. straight edge plus visual inspection .. Repair shops should have a laser tool specifically designed for checking pulley alignment.... Keep in mind IF a new belt is operated at all on a misaligned pulley system, it is not going to run true even if the alignment problem is resolved! .. A NEW belt MUST be installed after the final repair.