The more time passed, the more sure I became she’d [...] me.
The most common word in this case is reject. I'm wondering, though, what euphemisms I can use aside from turn down?
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You can say "She spurned me", though that's typically a very conscious, deliberate, and negative action.
From Collins, for example:
spurn: to reject (a person or thing) with contempt
So you would not be uncertain if the woman spurned you (she would make sure of that).
For a more passive rejection, one where she simply isn't reciprocating your affections, you can say "My love went unrequited".
From Collins again:
unrequited: (of love, affection, etc) not reciprocated or returned
Though you can see this phrase has the drawback about taking about your love as the object, rather than the woman or the relationship between the man and the woman.
Somewhere in the middle between passive and active rejection, in a way that talks about the relationship between the man and woman, is the construction:
The more time passed, the more sure I became she’d dismissed me.
The drawback to dismissed is that it is not specific to love or affection (though your readers would understand that's what it meant in this context, i.e. the elided clause [... as a lover] would be inescapably implied).
In regards to your "vice-versa", I'll caution you that turning the question around, and not-requiting a woman's love, is, to put it mildly, risky:
Heaven has no rage like love to hatred turned, Nor hell a fury like a woman scorned⁵
aka Hell hath no fury like a woman scorned
-- William Congreve's character Zara, in his play The Mourning Bride (Act III, Scene VIII).
A number of indirect or figurative expressions for rejection exist, but I can't think of any single-word alternatives that aren't either just as brutal as "rejected" (for example, "dumped") or excessively vague ("released").
Here are some phrases that describe the process of rejection in indirect or metaphorical terms that may border on euphemism (I made up these examples; hence no attribution for what looks sort of like a block quote):
The more time passed, the more sure I became that she was giving me the cold shoulder.
The more time passed, the more sure I became that she’d decided to try her luck [or test the waters] elsewhere.
The more time passed, the more sure I became that she’d made up her mind to put me in the rear-view mirror [or put our relationship on permanent hold or move on].
Perhaps, disregard works irrespective of the man-woman and vice versa situation.
[WITH OBJECT] Pay no attention to; ignore:
‘Jamie disregarded Dougal with a shrug and pushed on the golden rod to the door.’