Sony Walkman / USB not working with larger files

I have an old Sony Walkman mp3 player and it works fine when copying mp3 songs and listening to them. However, when I try to copy larger files - talks of one to two hours in this case - the files fill cause trouble firstly in playing them at all with the Walkman and secondly the sound will be just glitches.

With my memory stick the Thunar eject button works ok, with the Walkman it doesn't so I use right click -> unmount.