I am assuming by the syncro sleeve he is refering to the slider. If so you can see if the ends are all chewed up, but more than likely it will be the brass syncro itself. The brass syncros are made to be sacrificial (brass is softer than steel) make sure all the dog teeth of the syncro are good and all the dog teeth on the gear are good. The should be sharp looking not with a smooth face. It sounds to me like the syncro is not grabbing the gear enough and that can be due to the oil not being GL-4 rated. If it is GL-5 it has too many friction modifiers in it and it is too slippery and won't let the syncro grab the gear hub.
Hope this helps.