Simple question.  Simple answer?  Yes.

But what about people thinking you haven’t prepared something fresh so you are just reworking old material?  What about the feeling of deja vu that will overcome the listeners?  What about?  What about?

As a preacher you have to answer to God for your preaching ministry.  If you think the church needs that passage again, why not preach it again?  What people might think about your ministry or effort is very much a secondary issue.  You can make it clear that you are not trying to sneek a repeat past them.  Tell them upfront that you have preached it before and that you feel before God that we need to think it through again, or some more.

Personally I would be very willing to return to the same text for a second service on the same day.  It allows for deeper levels of application and reinforcement.  I would be willing to return to the same text after a gap of weeks, months or years, too.  Perhaps it helps to think about it this way:

A sermon event consists of several ingredients – the preacher, the listeners, the situation, the text.  When time has passed, the preacher is not the same person they were before.  The listeners have changed (individually, and in respect to who is actually present).  The situation has changed.  The text remains the same, but is engaged by the first three elements in a fresh way.

Same text, different occasion, why not?  Our purpose is not to impress listeners with new information week after week, but to shepherd people before God as under-shepherds . . . sometimes the same patch of grass is what they/we really need!