Sounds like something either locally, with your PS4/PSN connection, or something upstream on your ISP's network is causing some sort of connection reset. PSN itself has been having stability issues with the PS4's since release, could be at play here... as you are relying on your PSN connection to play.

Have you noticed whether your modem goes into any kind of reset or rebooting routine when this happens? If you can access the modems logs, you may see a pattern forming with a lease renewal or something else going on at the same intervals--could be a signalling problem on the other side of your modem caused by something between you and the termination system of your ISP (or possibly your modem is dying a slow death).