I initiated a payout at 06.07.2011 17:37 server time, it is now 06.07.2011 23:59:23. I see the payout on the payments page, but it has not even showed up as unconfirmed in my client.
There is no fixed "server time", you can select any timezone in your advanced settings. Default is UTC(GMT).
If you see your transaction on the payments page, then you shouldn't worry - it WILL be delivered.
I don't know about any case when it wasn't. Sometimes after server restarts or other affecting events some payout chains are not included by our pool and it takes up to a few hours more to confirm. But it won't be lost.