The policy depends on the XMPP server you are using. On OneTeam.im, the server does not allow to keep session for so long because it can be a security problem. Imagine you stay on for 7 days and join a heavy traffic groupchat: The server will have to buffer tens of thousands of messages. If you do that for many users, you could kill the server.
If you buy the module for ejabberd to deploy push on your own server, you can use whatever policy you want and if you want to risk killing your server or trust your users to do the right thing, this is up to you.
As I said this is a domain owner policy.
Of you run your own ejabber and buy the push module for Oneteam, you can define the policy you want and take the risk you want.
Note that you have the same security risk on the server with one to one chat. In 7 days you can receive a huge number of messages, legitimate or resulting from an attack.
So to summurize, run your own service and domain to solve your problem and use the policy you want.