This seems to be the cause of endless discussions, many freewheels tossed on the trash heap, and countless hours spent adjusting derailers. One possible simple cause should always be checked first.

Look at the spacer between the smallest sprocket wheel and the next one.

If you see shiny wear marks, as in this photo, the bike may have been provisioned with a chain (often issued as original equipment on many low end bikes) that is really meant for 1- and 3-speed bikes, even if it has 3/32" rollers. It has larger plates around the joint pins that cause it to ride too high in the sprocket valleys, allowing the teeth to catch the rollers and heave the chain forward a link under stress.

Here is a brand new Shimano freewheel on a Giant Cypress ST that was experiencing chain skipping, with its original chain:

You can see from the light between the chain and the sprocket that the chain is not fully seating.

Here are three random chains from my junk box. All have 3/32" rollers and 1/2" pitch, but they all have different inner plate maximum diameters.

The chain plate diameter is not a specification that is published by any chain manufacturers!
Replace that chain with the top one in this picture and your problems just might disappear.