In theory, if you were worried about this, I think you could get around that problem by just constantly send fixed sized encrypted messages large enough to hold any potential notifications. When a notification needs to get sent, you add it to the next outgoing encrypted message. Of course, now the delay for notifications is now coupled to the rate of these messages being sent.
The messages can still be traced to the client picking them up. Cut their networking and the client doesn’t receive the messages anymore… this shows up as a bounced message.
You can accumulate encrypted messages at random urls instead
If nobody in the chat room can know that you lost connectivity, that means you can't do real time chat and might as well use email instead.
Note that a similar thing happens with any two-way conversation; if an immediate reply is expected and there's no reply, it's not a conversation anymore. (For more possible reasons, though.)
Disappearances can't have good error messages if you want plausible deniability. This will make any UI much less user-friendly.
Simply use free Usenet Servers via Tor and post your anonymous* PGP
messages to the Usenet group alt.anonymous.messages.
*You send PGP encrypted messages via Mixmaster Remailers (via Tor) and
preferably use a hashed subject (hsub) so that the intended receiver(s)
can filter out their messages.
> A police unit parked outside a guy’s house and confirmed it was him in the real time chatroom, by cutting his internet and seeing him drop off.
I guess I'm going off of too few details probably, but this doesn't seem like a very sound strategy to me. It's certainly not impossible that the real criminal lost internet around the same time as some suspect's was cut by the police. I know I've shown up as online to other people for up to several minutes after losing internet in real-time situations (e.g. games). I suppose police just need "reasonably likely" to take action though, not definite reasons.
A police unit parked outside a guy’s house and confirmed it was him in the real time chatroom, by cutting his internet and seeing him drop off.
If you want real anonymity on the Internet, never use push notifications. Always “pick up your mail” periodically from random endpoints on the Web.