From the spec —
7.14 Exiting a Room
In order to exit a multi-user chat room, an occupant sends a presence stanza of type \"unavailable\"
Yes you can make your group persistent by setting its configurations this way:
NSString *var = [field attributeStringValueForName:@"var"];
if ([var isEqualToString:@"muc#roomconfig_persistentroom"])
{
[field removeChildAtIndex:0];
[field addChild:[NSXMLElement elementWithName:@"value" stringValue:@"1"]];
}