Scenario 1) The universe will end in heat death, the big rip, or other similar cosmic catastrophe.
Scenario 2) The universe continues on for infinity, giving plenty of time for even the most ridiculously unlikely of events to occur. It is therefore inevitable that humanity or whatever progeny it might have will still ultimately cease to exist.
Scenario 2 isn't actually so clear. Over time, humanity can decrease its suceptability to being wiped out by unlikely events at a faster rate then the events themselves over time.
Already failed then.
Scenario 1) The universe will end in heat death, the big rip, or other similar cosmic catastrophe.
Scenario 2) The universe continues on for infinity, giving plenty of time for even the most ridiculously unlikely of events to occur. It is therefore inevitable that humanity or whatever progeny it might have will still ultimately cease to exist.