Just a theory, really.
Could it be that Trinity had given up hope on finding the Chosen One and Cypher convinced her to be his operator while he made a deal with Agent Smith?
Why I think it's possible:
There is an unclear history between Cypher and Trinity. Maybe he made an advance and she rejected him, but was still interested in going back to live in the Matrix.
MAN (V.O.) Yeah?
WOMAN (V.O.) Is everything in place?
TRINITY (WOMANV.O.) I said, is everything in place?
CYPHER (MANV.O.) You weren't supposed to relieve me.
TRINITY (V.O.) I know but I felt like taking a shift.
CYPHER (V.O.) You like him, don't you? You like watching him?
TRINITY (V.O.) Don't be ridiculous.
CYPHER (V.O.) We're going to kill him. Do you understand that? He's going to die just like the others.
TRINITY (V.O.) Morpheus believes he is the One.
CYPHER (V.O.) Do you?
TRINITY (V.O.) I... it doesn't matter what I believe.
CYPHER (V.O.) You don't, do you?
TRINITY (V.O.) If you have something to say, I suggest you say it to Morpheus.
CYPHER (V.O.) I intend to, believe me. Someone has to. The final NUMBER POPS into place --
TRINITY (V.O.) Did you hear that?
CYPHER (V.O.) Hear what?
TRINITY (V.O.) Are you sure this line is clean?
CYPHER (V.O.) Yeah, 'course I'm sure.
TRINITY (V.O.) I better go.
In this scene, Trinity seems to snidely remark on Cypher's regard for Neo.
CYPHER There's something about him, isn't there?
TRINITY Don't tell me you're a believer now?
CYPHER I just keep wondering if Morpheus is so sure, why doesn't he take him to the Oracle? She would know.
TRINITY Morpheus will take him when he's ready.
Maybe her coldness towards Cypher was an act to protect Neo and atone for her transgressions.