I guess it's a regional thing because I Googled "running roses" before asking and couldn't find anything.
I have two climbing Queen Elizabeth roses and they both rebloom, although not as frequently as the grandiflora QE. HMF is wrong to call it a once-bloomer.
They're actually quite common, Sue. You probably have seen them a hundred times in nurseries and didn't notice the "Cl." following the name. You've seen mine a hundred times, for that matter. One of them is the huge rose that covers the back fence behind the Climbing Happy pillar that DrDon made for me.
Cindi, I think "shrub rose" is used primarily as a catch-all phrase for any rose not meeting the specifications of other classes. Most of the Buck roses and almost all of the Austin roses are shrubs, for instance, because they don't meet the requirements for hybrid teas, grandifloras, or floribundas.