Does anybody know how long it takes for a vendors inventory to change.

between 3 days to a week (in game obviously)

HOWEVER, apart from a handful of merchants, a few have a bug where their inventory does not update.

For me, the reliable merchants are

Gun Runners
Arms Merchant at 188 Trade Route
The guy at the Goodsprings store ( I can't recall his name)

Try this fix: http://newvegasnexus.com/downloads/file.php?id=37107