Rafael's "memento mihi semper." may be worthy of further study. In a discussion on "indirect objects with transitive verbs" Allen & Greenough (p362; reprint p225) give the example "equo ne credite" (Aen. II. 48) = "put not your trust in the horse"; which appears to support the use of "mihi" (the dative) as an indirect object, coupled with a transitive, imperative verb. (A & G give "credo" as able to function as both a transitive and intransitive verb.)
The problem is that the sentiment expressed: "Always remember me." is something that would be said by a partner in, or about to leave, an emotional relationship. Again, Allen & Greenough (p350; p218): "Memini takes the genitive when it means to be mindful or regardful of a person or thing, to think of somebody or something (often with special interest or warmth of feeling):
"nec me meminisse pigebit Elissae, dum memor ipse mei" (Aen. IV. 335) =
"nor shall I feel regret at the thought of Elissa, so long as I remember myself.""
At the opposite end of the relationship spectrum, a casual acquaintance (A & G same page): "Memini takes the accusative when it has the literal sense of retaining in the mind what one has seen, heard or learned. Hence the accusative is used of persons whom one remembers as acquaintances, or of things which one has experienced:
"Cinnam memini" (Phil. v. 17) = "I remember Cinna.""
The accusative (casual acquaintances), the genitive (emotional relationships) but (A & G) do not offer any examples of "memini" plus the dative. Therefore, what is to be made of "Memento mihi semper"?