I had a similar problem years ago with an old turntable, played most records under 3 minutes perfect, on other tracks a little longer it would stick towards the end of the track,
found out there was a small spring on the underside of the tonearm, some kind of compensator/antiskate device but it restricted movement towards the end of the track, even when I
pushed the tonearm towards the centre of the turntable manualy you could feel some resistance from the spring pushing it back,
I stretched the spring a little very carefully with snipenosed pliers, problem solved on my tonearm.
Hope this makes sense, he could try this by raising his tonearm with the cue lever and gently pushing the tonearm towards turntable centre to see if there is any restrictions.