What is the origin / history of "can't seem"?
Solution 1:
Well, structurally it should be “It seems that I can’t X”. In all likelihood “I can’t seem to X” is just a shorthand for that, even though it’s technically weird.
This may be an example of verb raising. Other examples of this include:
I want you to do X (instead of I want that you do X): semantically, you is the subject of the X, but syntactically it is the direct object of want.
Bill is certain to win (instead of It is certain that Bill will win): semantically, Bill is the subject of win, but syntactically that of be.
Bill is tough for Carol to convince (instead of It is tough for Carol to convince Bill): semantically, Bill is the direct object of convince, but syntactically the subject of be.
Solution 2:
The construct is a bit odd, but the meaning of "seem" is the same. "Seem" refers to perception (how things appear to the speaker). "This room seems cold"/"You seem tired"/ etc.
"I can't seem to..." means "I perceive that I am unable to..." - there's no change of meaning, although "It seems that I cannot..." may be a clearer way of expressing the sentiment.
The actual etymology of "can't seem to" is difficult to trace but this Ngram shows that it seems to have first occurred around 200 years ago and has since become far more popular in usage than "seem unable to":
