PSN has been having issues off and on since PS4 launch. They had a big maintenance recently to try to address their stability issues, but it looks like there are still problems. May want to give their forum/facebook/twitter pages a shot. Here's a map from downdetector showing reports over the last 24 hours:
http://downdetector.com/status/playstation-network/map/
It also provides links to their twitter and facebook pages, as well as a link to their PSN status page where you can get a link to their forums. Here's the front end page for their forums, just click the link for your specific console to get to it's threads:
http://community.us.playstation.com/...ort/ct-p/10023
There is a thread in the PS4 forum that may help you decipher some of the error codes if you are getting one specific to the console or PSN:
http://community.us.playstation.com/.../td-p/42154857
The Down Detector site tracks a lot of web services. You may even find one for your ISP as well:
http://downdetector.com/companies
It should be noted they've also been tracking similar issues with XBL users as well... in some of the same areas some of the ISP's have been having issues. For example, if you compare the Time Warner reports, you may see some of the same areas in the US reporting problems that are also showing up for PSN and/or XBL. So, it could very well be an issue with the ISP's responsible along your route that are causing some of the problems.
So, if it isn't something console or PSN specific, you may want to check to see if it isn't the already established very common issue of high congestion/packet loss in route that is cropping up along your route that your localized support for your ISP may not have been able to identify. If you weren't providing them enough information to properly analyze your connection to SE or any other remote service, all they are going to be able to do is look at your local nodes---not something a dozen hops down the line in somewhere like New York, Ohio, Chicago, or Canada. Those Tier1 guys at the support desk and most of the Tier2 guys that come to your house typically won't be looking much further than your local nodes---a very large number of people are running into stability issues upstream, as in another state or even another country.
To track such issues down, their Tier3/Tier4 guys will need to get involved and will need at the very least the IP of your game server to run diagnostics against. Ideally though, you should provide them with trace reports showing the route(s) you are taking to the game server or any other services you may be having issues with (like Netflix, Google/youtube, yahoo, etc.). Hopefully it will capture signs of congestion or packet loss along the way giving them a hit of where to look further into your problems.