That translation always confused me. Here is my translation of Duty.

Basically, Ayu is saying that we are all searching so frantically for something to complete us, that we don't realize when we have already found it.

My interpretation of the song is that the "thing" we all want is happiness and fulfillment. In the first verse, this could be understood as a situation in which a person is so focused on the future and self-betterment, that he/she takes for granted all the happiness and success already achieved.

In the second verse, she talks about how this "thing" lines up and connects people's memories. This could be understood to be the sort of happiness and fulfillment found in relationships (the bond of memories between two people). She says that, if we already have this bond of memories (which we all do), shouldn't we already be happy?

As far as "the end of an era", I think she is talking about growing up, and realizing that it is now your turn to go out and find this happiness on your own, rather than having someone else do it for you like when you're a child.

The bridge demonstrates that this security may be what Ayu really craves; to just surrender this heavy responsibility (or "duty") to someone else who will take care of it for her. This makes sense for a perfectionist who pushes him/herself to such a limit, that even he/she needs just one moment without having to worry about everything alone.

If you analyze the Japanese in the bridge, it has the connotations of:

"If it's you, you'll find it for me."

Or more clearly:

"You're the one who will find it for me."

This shows that Ayu isn't prepared to surrender this duty to just anyone; she would rather take care of it herself. But she is holding out for just one person who she can depend on to take the weight off her shoulders, because she is actually terrified of the tasks she takes on so bravely.