I've changed my answer. To summarize, drop in means to arrive singly, in this case after the main mass of visitors.
If I'm right, and this is the meaning, then to drop in for an after-loss would mean to make an appearance after all of the poet's other misfortunes and cause a final misfortune (an after-loss).
Paraphrasing: "if you're leaving me, give me the bad news now, when I am beset by all my other misfortunes, and don't wait and tell me later."
Why do I think this? To find what Shakespeare meant by the intransitive phrasal verb drop in, we need to look for other uses of it in Shakespeare's time. Shakespeare appears to be the first to use drop in with anything near this sense. But here is an instance of drop in from the book Of the Head-Corner-Stone, by Edmund Bunny in 1611, only two years after Shakespeare's Sonnets were published, and one or two decades after they were written:
… but that divers of the Israelites (such as shog’d aside for the time, to avoide the danger of the enemies Sword, and afterward came dropping in againe)
The relevant meaning of the obsolete word shog here seems to be to move to the side or to go away. So these people went away to avoid the danger, but came dropping in when it was safe.
The meaning of drop in here seems to be the OED's definition
- intr. To come in one by one or at intervals,
which the OED has first attested in 1697.
There is also another use of drop in with this meaning in the 17th century, that the OED seems to have missed. From 1668:
Other vessels are dropping in; 25 colliers passed by Bridlington, and as many lie in the bay for Newcastle, expecting a fair wind.
This is not so far from the modern meaning to make an informal or unexpected appearance at somebody's house, which is first attested in The Diary of Samuel Pepys in 1667:
At noon dined at home, and Mr. Hater with me, and Mr. Pierce, the surgeon, dropped in, who I feared did come to bespeak me to be godfather to his son, which I am unwilling now to be, having ended my liking to his wife, since I find she paints.
In fact, looking at this quote, it's not clear to me whether drop in here has the modern meaning of to make an informal appearance or the meaning of to arrive singly, after the meal has started. So it's easy to see how the arrive singly meaning turned into the make an informal or unexpected visit meaning. If it does indeed mean arrive singly here in Pepys, it's very similar to Shakespeare's use of the phrase.
To answer some of the rest of your questions:
Who is dropping in?
The thou of the poem.
What does in relate to?
Drop in is a phrasal verb here; in is a particle, not a preposition.
Tsundoku has a different answer, in which he explains everything that was wrong with a previous version of my answer. Let me try to explain why his interpretation (which follows a suggestion of John Kerrigan) is probably incorrect.
- He claims that drop in means fall upon, based on a single use of drop in from Antony and Cleopatra. The use of drop in from Antony and Cleopatra is transitive, while the use in Sonnet 90 is intransitive. To see why this makes a difference, let's look what happens when we substitute fall upon in Sonnet 90:
And do not fall upon for an after-loss:
That's horrible—fall upon needs an object after it.
- The meaning to arrive singly fits the sonnet's theme extremely well. Furthermore, this meaning of drop in is associated with drops of water, which arrive one at a time, and the line
Give not a windy night a rainy morrow,
echoes this theme of water droplets. The meaning to fall upon does not fit as well.
Summary of my previous answer:
For completeness, here is the main argument from my original answer:
It seems to have meant something like "to make an appearance on the scene" in Shakespeare's time. Did it need to be an unexpected or informal one? I can't tell, but I think it's quite likely. Both Shakespeare's use and another contemporary use1 I found of drop in could easily have the connotation of informal or unexpected.
1 Bunny's given above.