EDIT: All services have been restored, and everyone seems to be able to connect as usual. The original story is below:
There appears to be an issue with several ISPs/locations connecting to PSO2 servers and the website. SEGA has announced that they are aware of the problem and looking into it, and apologies for the inconvience.
http://pso2.jp/players/news/21909/
For those who can't access the page, it essentially says "Currently, there is an issue where players cannot connect to the server and website. We are investigating the cause and a fix. Until it is resolved, we apologize for the inconvenience. Please be patient until functionality is restored. Thank you."
Update: SEGA has updated the above link with further details about their "fix":
2018/7/2 18:30更新 7月2日（月）15:50頃より、ゲームサーバーおよびプレイヤーズサイトの一部ページに接続できない現象が発生しておりましたが、16:25頃に復旧いたしました。 現在はデータセンターおよびゲームサーバーで問題は発生しておらず、正常に接続できることを確認しております。 また、復旧以降も一部の回線で接続できないとのご報告をいただいております。 こちらにつきましては、ご利用されている回線で障害が発生している可能性がございますので、ご利用されているプロバイダ様へお問い合わせいただきますようお願いいたします。 皆様には大変ご迷惑をおかけいたしましたことをお詫び申し上げます。
Translation: "Around July 2nd at 15:50 JST, there was an issue where it was not possible for some people to connect to the game server and website. This issue was resolved around 16:25 JST. Currently, there are no problems with the data center or game center, and we have confirmed that we can connect normally. We have also received some reports that people cannot connect after this fix. Because of this, there is a possibility that a failure has occurred in the connection being used, so please contact your ISP. We apologize for the inconvenience this has caused everyone."
However, numerous regions and ISPs (including some of the Japanese players) still cannot connect to the game or the website. We are hopeful that this is a temporary issue and will be resolved in a timely manner. We'll update this post as this situation develops.
Update: All services have been restored, and everyone seems to be able to connect as usual.