As with so many "rules" about English grammar and usage, this one isn't in fact a rule.
I have liked pasta since I was a baby.
implies that the speaker still likes it. However, the sentence:
I have liked pasta since I was a baby, but now I can't stand it.
denies that implication, without in any way changign the grammer of the first clause. Furthermore a sentence such as
I have liked pasta -- on rare occasions.
certainly carries no implication of continuing liking, but the grammar of "have liked" is unchanged. That this form shows a continuing action is the defaiult state of things, but only until context indicates otherwise.
I have been to this place before.
does not in any way imply that this is a continuing action. I am not sure if the verb would be labelled "stative" in this usage, and I am less concerned by such labels than by the overall meaning of the expression.