This may be worn index springs, but that usually shows up first in low gear where cable tension is highest and works down from there as the springs continue to weaken. I usually have no problem causing an upshift in the lever by pulling the wire away from the frame, but as the springs weaken this gets easier.

However, if you don't notice the lever clicking by itself, and if the slippage is happening in any gear, there's a good chance that the problem is simply trim that's adjusted slightly outboard of center. Folks do this when housings get a bit worn or dirty because the RD spring is sluggish making upshifts. That improves the shifting, but at the cost of what you're experiencing.

One test for sticky housings is to upshift, then pluck the wire at the downtube. If the sudden snapping action moves the RD out a bit more you have sticky cables. The solution is to fieldstrip, clean and lube cables or to simply replace them if they're old. Be sure to cut the rear loop long enough that it comes into the RD adjuster straight on.

BTW- while you're there, take a quick look at how the rear loop lines up with the adjuster. If it leaves at an angle, that could be the problem right there.
Test by using a rubber band to flatten the rear loop so it lines up better and see if things improve. If so, you can either replace the rear loop, or leave the rubber band in place, though half your buddies will ask why it's there.