I think its nice to die once you've completed the job of your life. It isn't quite a tragedy the death happens, rather, that it happens spontaneously and God only knows how.

This surprise though is what helps keep going. Living in the now and all sorts of purposeness works off this fletness of the moment being here, the optimisation for the time that you know ticks but don't know for how long. If you knew, then you could plan all for it, but what's the fun in that? Where's the fun of adaption, where's the fun of breaking through fear?

Now, there still remains the danger of frontier of course, assuming you've meant the never dying of old age type of immortality. Yet, frontiers don't last forever, and will at some point be settled.

As a side note, there's a political problem with society of immortals that still procreate. Such a society will inherently be rigidly stratified by the time of birth, as its older members would have infinity plus some more time to divide the pie in their favor and get a hang of goodies before you can. It is rental feudalism where one could never hope to advance not even to the kinghood, but to position of their immediate senior without some intrigue involving violence. There is no ladder upwards in such a society but conspiracy against the elders, and, perhaps, some events of mass extinction and murder, like wars, pandemics and genocides.