Nor Mars his sword nor war's quick fire shall burnThe living record of your memory (7-8)
The only way to escape the violence of the future is to just keep living. And Sonnet 55 is doing just that, sitting tight in the memories of every reader as the rest of civilization goes down in flames.
[…] all posterityThat wear this world out to the ending doom (11-12)
But time doesn't only bring destruction. Okay, so it's no Easter Bunny, but after enough centuries time will eventually bring the end of the world and the final judgment. That sounds bad, but only if you are also bad. If you've lived a good life and never cheated on your SATs, you'll be resurrected into an eternal life of harps and happiness.
So, till the judgment that yourself arise,You live in this, and dwell in lovers' eyes (13-14)
The speaker makes it clear that his beloved is definitely on the train to heaven. But until the time that God brings him physically back to life, Sonnet 55 has to keep the poetic oxygen pumping, making sure his memory doesn't fade even if his body has kicked the bucket.