Christ is risen!
I can't remember who wrote this (it might've even been someone here!), but somewhere I read "we say 'Lord, have mercy!' forty times because we don't mean it until the thirty-seventh time". That really struck a chord with me.
I personally love hearing "eti kai eti" / "again and again" at the beginning of each of the litanies, because it gives me an opportunity to pray again for the things I didn't pray for fervently enough the first time. I especially love the "antilavou, soson, eleison" / "help us, save us, have mercy on us". I never get tired of repeating that one!
But you've said you already understand this aspect of the issue, so I'm not sure how helpful that is. Hmm ...
There's also some hardcore academic discussion out there about the structure of the liturgy and how it is not linear, but spiraling/looping -- which gives a sense of being outside of linear time, in eschatological time. In God's time, really, where nothing happens just once but is constantly happening. I think this is also why we Orthodox speak in the present-tense about things that have already happened in historical time: "Christ IS risen".
Can't say my dilletantish mind really grasps such things.