I have long disagreed with the common interpretation of this sonnet. Although I agree that the images of night, bare trees, etc., are symbols for the passing of time, and that "Death's second self" could simply be a reference to this, I cannot help to think that this poem is about self-love, not the love of another. It is about the sadness of knowing that even the most brilliant of minds can wither and slow down with the passing of time.
Consider these lines as a whole:
"Death's second self, that seals up all in rest.
In me thou see'st the glowing of such fire,
That on the ashes of his youth doth lie,
As the death-bed, whereon it must expire,
Consumed with that which it was nourish'd by."
Death has two states: Its approach and its presence. A mind also only has two states: Thinking and the inability to think. Thinking - his driving life force - marked the speaker’s life. Age slows the mind and even 'death' can appreciate a well-used one.