Stable public jabber server?

If you need reliability, then use the big three (Gmail, yandex, qip), or localhost. The experience of everyone I know on other servers sooner or later have to change the server.
In the aspect of conferences, Gmail, throw, of course. There are two above, which someone for some reason put red.

Gmail.com keep a history of correspondence

It can be disabled.
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there are automatically added contacts

In the GoogleTalk client may not know Miranda in my roster only those I added.

yandex?

Use jabberon.ru — the guys are good and passionate about. Always something new added from the transports, already quite a large selection. The inaccessibility were a few times when DC was burned and when the new server was already moved to another DC... And so the special problems and not remember.

I use Hohlovym the Jabberwock. Your requirements is your own jabber server. Little sooner or later will crash/close.

Use https://404.city/
Stable server, failures were noticed. Does not store history