I wouldn't exactly describe what U1 and U2 are doing as "dying", any more than if U1 could somehow continue to exist in perpetuity -- if you were frozen in stasis forever, for example, such that you never got to the end of this comment -- I would exactly describe that as "living". Our normal understanding of life and death is defined by the continual transition between one state and another; those terms don't apply too readily to conditions like indefinite stasis.

But, terminology notwithstanding, if the passage of time constitutes the destruction of the same value that using a hypothetical transporter does, I'm not sure how your original thought experiment holds up. Why not use the transporter, in that case? Refusing to doesn't actually preserve anything.

As for reasons to stay alive... well, that depends on what we value.

There's a vast set of possible histories. In some of them U1 ceases to exist and U2 comes into existence (what we normally call "you stay alive"), in others U1 ceases to exist and U2 doesn't come into existence (what we normally call "you die"). Do you have a preference between those?

A different way of putting it: there's a vast set of possible U2s. Some of them are living beings and some of them are corpses. Do you have a preference between those?

EDIT: Whoops! I just realized that I got your OP confused with someone else's comment. Ignore the stuff about the transporter...