How much is getting past? Is it a gusher, like when you empty the tanks, or is it a tickle?
If it's a trickle, it could be a bit of residual water left in the pipe that didn't drain out completely. You put the cap on and there was still some fluid in the pipe. I know, that just doesn't sound right, but sometimes they can drip for a while after the valve is closed. There is some distance from the valve to the end of the pipe.
Or...
The slide valve is not closing all the way. Toilet paper, gunk, or anything could be caught in the slide valve, where it seals in the track. If this is the case, then...
One thing you can try to do, is empty the black tank and flush it out by backwashing (if you can do that), or black tank flusher, or with a toilet tank wand down the toilet. Clean the tank out, and get it as free of "gunk" as possible. Now that it's cleaned out and empty, fill the tank with about 5 or 10 gallons of water. Make sure the valve is closed. Make sure the cap is on the end of the outlet. After adding the water, move the slide valve in and out several times. What you are trying to do is clean off any gunk that may be caught in the groove the slide seats in. The reason for the clean tank is to ensure no new "gunk" will get caught in the slide valve. Sliding back and fort several times (might) clean it free. Now, open the end cap and let the "gunk" run on out (and hopefully it's not too nasty.)
If that does not work, they do make some products to help clean the slides by adding it to the tank water. I've tried a couple of these, and found them not to be very effective. Vigorously moving the slide back and forth did more good than anything.
And there is a third possibility. The valve is sealing good, but when traveling, it wiggles open. I can't imagine this happening, but if the tank is empty (they are never truly empty) there would be no back pressure on the valve allowing for it to slide. Or it's possible, if your slide is operated by a cable, the cable is not letting it shut all the way.
FYI, even though your tank may appear to be empty, as soon as you move the camper, the fluids on the bottom of the tank will move around and eventually find the outlet. As said, there is always some left in the tank, unless you can turn the camper on it's side and shake it out.
Try cleaning the slide first with the water method. See what happens. There's no cost involved there, and I'm a firm believer in doing the least evasive "thing" first.