A Question on External Hard Drives

I wonder if anybody can shed light to this particular problem I’m having with my 500 Mb USB external drive. Because I watch tons of TV shows, mostly in marathon mode over weekends, an online backup of files won’t work for me. I need a storage that I can access readily anytime. 

When I bought my external hard disk, the intention was to use it to connect with my DVD player so that i won’t need to burn them into DVD media. With a little research, I discovered that the default file system format of the drive was NTFS, but the DVD player will only read from a FAT-32 drive, so I converted. The question now is this: Whenever I use it to connect with the DVD player, it almost always stop in the middle of my “watching session” so I have to look through the file folders again and search for the part where the video stopped. It’s like having to restart your PC several times just to finish watching a clip of one TV episode. It’s a bit tiring, and although I’m a pretty patient person when it comes to this stuff, I would appreciate it if I can learn that there’s a way to remedy this problem. So is there?