Hi, Jeff... Reptile is on the right track. It sounds like the axle is protruding too far, particularly if the axle has been replaced. There have been plenty of "standards" over the years- there's no easy way to tell without looking at it carefully. One test is to take the skewer out and remove the spiral "volute" springs. They can get in the way. Put the skewer back in and tighten it down and see if that fixes it.

If it does, then there's a couple options: shorten the axle by 3 or 4 millimeters, put washers between the cones and locknuts, or just do without the springs. They don't do much except make it easier to put the wheel back in the dropouts.

Also, if it's an aluminum-handle exposed-cam skewer- toss it and get a good steel, closed-cam skewer. They work 1000% better.