I have an ancient Raleigh hybrid. I've had a few issues with the QR slipping on the drive side, which has occurred with different skewers. Any suggestions other than 'just do it up tighter'?
Get a Shimano QR - even a Deore one will do.
It could be related to a misaligned frame or a twisted dropout. That said a shimano skewer should fix it. Thus kind with the internal cam: [img] 
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What kind of dropouts does it have? If horizontal dropouts, some sort of chaintugs could help.
Forward sloping dropouts. Wrong direction for a chain tug as far as I can see...
I've got an XT skewer around somewhere I'll put on. It has security skewers on at the moment but it's not exactly a big job to lock through the back wheel.
The Surly Hurdy Gurdy chaintug is designed to work with forward-facing sloping dropouts. http://www.tritoncycles.co.uk/components-c9/chain-devices-tensioners-c62/surly-hurdy-gurdy-chain-tensioner-p2625
security skewers on at the moment
I'd bet that's your problem, I use Halo hex skewers and they don't provide anywhere near the torque Shimano skewers do.
