I suppose like most of us I was taught to lift the file, or hacksaw, for the return stroke, or at any rate relieve the pressure on it.
Reading this thread it occurred to me that lifting the tool clear might do more harm than good, potentially chipping teeth, by the slight but many-times repeated hammer blow when you start the next cutting stroke.
I don't know if that's a likely hazard or not, but I don't recall ever reading or hearing it anywhere. Even if not it may make consistency of action harder.
Provided you let the file slide back across the metal, I don't see leaving it in contact as potentially any more damaging than for example the action of a shaping-machine on hauling the tool back for the next cut. On a slotting-machine, as far as I can see, there is no relief for the tool on the return.
Edgar Westbury, in his Lathe Accessories – How to make and use them, p.76, shows a simple keyway slotting-tool in which the cutter itself swings on a pin, rather as on a shaper. Personally I'd be more worried about using my lathe in the way he suggests (winding the saddle back and forth), than preserving the edge of a very simple cutter! I think the modern equivalent, like a miniature shaper that fits on the saddle or tool-post, also typically uses a rigid tool.
My copy of that book, by the way, is the latest… 1955, cover price 3/6.
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So perhaps we do worry a bit more than we need about filing; but better that than wear them prematurely.