Terabyte+ thumb drive limitations

.mkv video files over 80 in sequence copied to non-corrupt 1- or 2-terabyte thumb drives (formatted as either FAT32 or exFAT) yield "cannot render the file" errors when the thumb drives are plugged into 2 separate laptops (1 running Windows 8.1 and 1 running Windows 10) and a generic video player is used to open the files (there is over 650 Gb of free space on the thumb drives). These specific files open from the hard drives of both PCs and from a Western external hard drive without fault. Is this a thumb drive storage issue? How can this be fixed so that a great number of video files can be opened from the thumb drive itself and played? The "cannot render the file" files, when copied back from the thumb drive back to a PC's hard drive yields the error; these same files open and are playable from the original source. Is this an inherent limitation with Tb flash drives that I must accept, or is there a workaround (provide workaround resolution steps)