Nexus IGH reluctant to shift after applying load I ride a belt drive bike with a Shimano Nexus SG-C6001-8D IGH. I'm aware of the normal cable adjustment procedure (aligning yellow marks on the hub), I've done this.
When I ride normally, shifting is instantaneous and smooth. However, when I move off at lights, I usually use gear 3, and I've noticed that if I accelerate hard, the hub will not shift into gear 4 after I change it; instead, it only shifts after I go up to 5 (and then it immediately goes 3 -&gt; 5, so gear 4 is effectively skipped over). Sometimes it also happens that if I shift 3-&gt;4 and leave it there, without going to 5, 4 will eventually engage after 5 seconds or so.
I should point out I don't attempt to shift under load; I accelerate in gear 3, release pressure on the pedals, then shift and continue.
As said above, this 3-&gt;4-&gt;5 shifting issue only happens when accelerating. If I ride normally at a constant speed, those gears have no issues.
I know for a fact the shift cable needs to be cleaned, there's likely water inside, as when it was -5°C/23°F outside once, the cable froze in its housing. Could this issue be caused by the cable, or is it a hub problem? I suspect the cable but I'm not sure why everything would be fine when not applying load. For reference, I'd estimate the hub has at most 5000km/3000 miles on it.
Yup - I've had this exact experience on an Alfine 11.  If you pedal in smooth circles and maintain the pedal pressure, its possible to shift a long way through the gears before the gearbox catches up.
At that point the gearbox will quickly move across up to 5~7 gears in one quick movement, which can be a massive drop in pedal cadence and is able to upset the rider's balance.  I had a couple of close calls because of this.
Upshot, an IGH is opposite to a conventional deraileur, in that an IGH needs a brief pause in the power to shift UP (to a harder gear) whereas your common bike transmission needs the rider to let off the pedals briefly while changing DOWN to an easier gear/larger rear cog.
You can also try accelerating with a distinctly choppy pedal stroke, which may help the fast acceleration or sprint start.
I never figured out whether this &quot;delayed shift&quot; was bad for the gearbox or not.  Mine lasted around 15,000 km before shifting went unreliable, and while there were always tiny flakes of brass in the oil, it never became more or less, over time.

SEPARATELY  The other thing I've noticed with IGH, both my alfine and a couple of 3 speed nexus bikes at work, is that the yellow lines aren't perfect.  You might find the bike's shifting improves if you put a half-turn on the adjuster away from &quot;perfectly-aligned&quot; but it could be in either direction.  Try twiddling the adjuster on your next ride, and see if it gets better being not quite perfect.
Lastly, also remember these hubs need service - an oil change yearly or every 5000 km is the shimano recommendation.

As for water in your cable, yes its definitely worth fixing that.  The water will cause rust and/or will collect dust/dirt and add friction  This will make the cable's movement sludgier, to the point the hub's spring can no longer overcome the resistance.
You could unscrew the barrel-thingy on the hub end, pull the inner out of the outer, blast some compressed air through the outer and follow it up with solvent, then a day later drop some oil in and let it dribble in.  Clean the inner cable too.
This depends on whether the inner cable can be reinstalled.  The inner cable should slide through the outer with minimal force, if you have to tug it then its gunked.
Last option there is a replacement of the inner cable and outer housing.  Not hard but fiddly to get the length exactly right.
Keep your bike inside, or at least under cover over night at a minimum, to prolong its life.