Hello Joe,
Thank you for attempting to help, but there was a misunderstanding. This isn't a Lenovo forum, it's an Intel forum, so I shouldn't have used the word "upgrade" - the w530 from Lenovo comes standard with a 6205 AGN wifi adapter, and they let you "upgrade" to the 6300 for $20. It wasn't manually installed or messed with aftermarket. It is a brand new laptop and has had this problem out of the box.
I do have it working now, although it's not a "solution" per se. The routers that I have been having this problem with were a/g only routers. I had ordered a Buffalo dual channel air station router (WHR-HP-G300N) in order to take advantage of my new laptop's wifi speeds, and now that it has arrived the problem has disappeared.
I have had a stable internet connection in N-Only mode at 20MHz (130bps), and N-Only mode at 40MHz (300bps) for many hours at very high traffic. I haven't tested it too thoroughly in G-Only mode (54 Mbps), but it also appears to work fine so far. I was getting about 5-10 minutes of use before failure before, so I only bothered testing in G-Only mode for about 20 minutes; some people have claimed losing it after an hour or so.
If it's not a problem running in slower speeds, perhaps the 6300 AGN adapter doesn't play nice with old routers?