Thanks for the welcome.
Yes, the prices update. However an auction can close early and the snipe just sits there. Nothing in the page can make it read correctly or change status to 'ended' or 'lost'. the sole option is to look it up on 'My eBay', then cancel it. My preference is for something more dynamic, and my contention is that, if the auction is over, then neither the price, nor anything else about the snipe is valid.
The only way, it seems, to get the page to update correctly is to: After reviewing 'My eBay' manually cancelling invalid snipes, leave the snipes page and return to it.
I noted that syncing clocks will make the time to close counter run for a while, but it soon stops.
About auctions ending early, there is a thing in the support forum saying it isn't done because they're afraid a change at eBay will mess up their text parser. I've written parsers before, and it IS hard to hit a moving target. But if it can be written well enough to ensure that changes in eBay don't mess up the sniping itself, the rest is not rocket science.
Truth be told, I've seen a lot of complaints about this sort of thing in the forums, and nothing constructive by way of a response. Just bits about why it can't be done.
Now that it's known sniping can be done, I expect eBay will have one up and running before very long. It would be smart to get this thing working pro-actively rather than trying to plug the leaks after people start leaving for other services.