Tell me do you trade the bitcoins directly with the miners only and that too every time? I guess no.
Consider this what if there no gold left on the earth to be mined? The remaining one in circulation would still continue to change hands regardless.
Similarly, when no new coins are mined the remaining coins would keep on transferring from one person to another.
I think this is a wrong analogy. Bitcoin can't exist, or "change hands", without miners, while gold perfectly can. So, answering the question, we should rather concentrate on the motivation for miners to continue doing their job. And the motivation will always be there, as shown in the comments above.