Cancelling will likely not result in a refund of the annual fee. Most likely Harris Bank is simply trying to figure out why many new cardholders are making larger than expected purchases at the same merchant. Has anyone who has NOT used the card at Target experienced a fraud shutdown?
Even then, locked for a month without any sort of feedback from them is unacceptable. I'd still try to see if they could credit a month's worth of the AF at least if not outright cancel it.
FWIW my Premier card isn't locked but I haven't used it at Target nor tried to make $1000+ transactions with it anywhere else.