In addition to the type of skewer, as covered above, there are a couple other things that can cause insufficient clamping:

1) Check that the axle isn't too long - if it extends all the way out to the edge of the dropout or beyond then the skewer might be largely just clamping down on the axle end rather than the dropout; and

2) The skewer should have a serrated edges that dig into the metal of the dropout. Over time the serrations may have worn down and made the surface smooth and more likely to slip.