Yes they can die on their backs as their internal organs are the wrong way up, causing pressure where they shouldn't. Internal gases build up causing more pressure. I don't think there's a set time. One year our neighbour didn't shear at all, so with 2 fleeces on, especially when it was wet and the fleeces really heavy, we had to stand cowped ewes back up several times each day. Hold onto them for a while to let them burp etc.
The only cowped ewe we had was heavily pregnant, lay down and tipped herself over a molehill and her belly, so she couldn't get back on her feet.
Another time in Shetland, on a coach full of sheep breeders, we spotted a cowped ewe in a field. We made the driver stop and we all leapt out of the bus, taking to the field in our Sunday best. The poor ewe was so scared by the apparitions charging towards her that she flipped back the right away up before we got there and charged off up the hill.
So I suppose fat ewes could be prone to cowp, or those with heavy fleece, but I don't know much more about it.