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Out of curiosity, can you be more specific about how you take care of it?

For my 900, I don't remember the procedure. I just remember that I had some slipping and made a quick adjustment which didn't seem to do anything. The second time I did the adjustment, I performed it exactly per the service manual the the slipping stopped.

Don't recall the procedure for the 1300 but it's simple and covered in the service manual.

Scotch made the point a few posts back, that the key is to remember there are two sets of adjustment, both require a little slack and are independent of each other.

1)The pushrod, running left to right through the engine casings, has it's own preload / slack against the clutch, which is adjusted by the screw & locknut on the left end of the pushrod.
2)The clutch cable, has it's bulk adjustment set at the engine casing, only after the pushrod is checked / adjusted, and then fine adjustment is available at the lever end.

Yeah, I've done it by the book. It will need one more time as the plates break in I assume.
Being a devil's advocate on the other hand, just like with the manual tensioner, it's hard to do certain things 'by feel'.

which is a good point Stan, as the friction material wears fractionally to 'bed' to the steel, the clutch effectively shortens and places the pushrod under slightly more preload, which could (if the logic's correct!) initiate some slip that wasn't there before?

Yes guys, I know how it works, haha, I put it all together! I haven't revisited any adjustments since first start, now 700 miles on the odometer.
Actually, I did the clutch mostly by checking free movement of the rear wheel when the bike was on center stand. At first the wheel was spinning in neutral, so I went on tightening the push rod adjusting screw until it wouldn't spin much except for a very slight drag, so I could easily keep it still with my hand. I might need to back it off a bit now, then play with the cable. Will report once I get to it!

Well that explains your issue.

When the bike is in neutral, none of the gears are cogged in and the only thing driving the rear wheel is the oil film between the shafts and the uncogged gears. As the oil warms up, the oil viscosity thins causing the frictional drag to be less and that will reduce the spinning force on the rear wheel. Guaranteed, you have the clutch adjustment way too tight.
Some bike models have a very positive "feel" to the clutch actuation and others like most of the Kawasaki's have a mushy feel. All of my triples and this KZ have the mushy feel. When adjusted properly, the clutch lever should almost be willing to flop in the wind. It's a very soft touch between disengaged and the clutch lever ready to actuate the clutch actuator.