Let me get this straight...
So... LFS says it's downloading the skins... And says its downloading some of those more than once in a loop...
While it is downloading those skins you don't see any of the downloaded skins, but when you disco and reconnect to the server, you see the previously downloaded ones, but not the ones it hasn't finished downloading yet?
If so... I've had that problem once... There's a list of skins it's downloading in the player options (I think)... See which skins are on there, and try to stop them downloading (you can cancel the downloads by clicking them or something, can't really remember... When you've done that, turn automatic skin downloading to off, and connect to the same server again... Then disconnect, turn automatic skin downloading back on, reconnect, and for some strange reason, from that moment forth, it would simply download all the available skins for me. There may be a small bug in the automatic download functions, causing the skins to become corrupted, or the wrong message received when downloads finish. Most common for me were helmet skins not downloading correctly.