I would recommend a thorough check of the hard drive itself with a testing tool (unfortunately I have no idea what works on a Mac).
Crystal DiskInfo X64 works well on a PC. Your issue appears to be more from your hard drive than the player.
I put plenty of > 10Gb files up to 45Gb in size on external (and internal) HDD but they are NTFS formatted.
A few of the hard drive companies have software that will format, write and read in NTFS on a Mac if you look.