Is it legal for a landlord in the state of Tennessee to charge a tenant's debit card electronically (using information stored from a previous transaction) without the tenant's knowledge, presence (neither of card or card holder) or authorization?
The basic legal limits on card use are here. The law is framed in terms of an "access device", which includes debit cards, PINs, telephones and so on (there are other laws about credit cards). It does not include checks and the bank account information that might be used for a one-time ACH debit. Rule 1005.2(k)(1) defines preauthorized electronic fund transfer
A preauthorized electronic fund transfer under Regulation E is one authorized by the consumer in advance of a transfer that will take place on a recurring basis, at substantially regular intervals, and will require no further action by the consumer to initiate the transfer. In a bill-payment system, for example, if the consumer authorizes a financial institution to make monthly payments to a payee by means of EFTs, and the payments take place without further action by the consumer, the payments are preauthorized EFTs. In contrast, if the consumer must take action each month to initiate a payment (such as by entering instructions on a touch-tone telephone or home computer), the payments are not preauthorized EFTs.
So the answer is yes or no, depending. 2(m)(2) says
If a consumer furnishes an access device and grants authority to make transfers to a person (such as a family member or co-worker) who exceeds the authority given, the consumer is fully liable for the transfers unless the consumer has notified the financial institution that transfers by that person are no longer authorized.
The literal words here say one thing, and surrounding circumstances suggest something else. A landlord is a obviously a person, but a landlord has a different relation to one than a family member or co-worker does – the parenthetical suggests that this clause refers to trusted individuals. The importance of that is that if a landlord is a "person" in this sense, then you are liable unless you have told the institution that he is no longer authorized.
The same section on unauthorized use indicates ties that concept on forced access (robbery at gunpoint) or cards that are stolen or obtained by fraud, also a class of reversals of direct deposits. None of these concepts covers the described use, assuming that the initial acquisition of the device was not by force or fraud. The fact of using a device without explicit permission in some instance does not constitute fraud (which involves making a material knowingly false statement that the consumer relies on to agree to an arrangement).
The use in question is covered in 3(b)(1), under the rubric "Funds Transferred Covered" (i.e. whether the use is an 'electronic funds transfer', which is regulated):
A transfer from the consumer's account resulting from a debit-card transaction at a merchant location, even if no electronic terminal is involved at the time of the transaction, if the consumer's asset account is subsequently debited for the amount of the transfer.
These regulations are about your relationship to the bank, the question being whether you have a legal basis for making the bank absorb the loss. There is little chance that this law would make you not liable to the bank (i.e. they would be required to return the money taken from your account). There could be some recourse in case your agreement with the bank specifically prohibits recurring charges with a debit card, but it is unlikely that there is any such restriction. Assuming you did not previously put the bank on notice that the landlord is no longer authorized to charge your card, then you have no recourse against the bank.
Any recourse would then be against the landlord, where the specific issue is whether the charge is or is not within the scope of an agreement. If you use a debit card to pay rent and in some month you indeed owe rent, then the landlord has not torted you by charging the next month's rent. If, however, the landlord gets the idea that your bank account is a source of free beer money thus the use is not covered by an existing agreement, then the charge would be wrongful, and you can sue the landlord. I will assume (since you don't specify the purpose of the charge) that the charge is in connection with an amount owed by you.
There is no statute that requires specific "for each use" authorization of debit card charges: any such limitations would arise from explicit agreements between you and the bank, or you and the landlord. If you have such an agreement, say with the landlord, which says that the use of the card is a one-time use, then only a one-time use is authorized. Otherwise, there is no implicit requirement that each and every transfer must be specifically authorized. Informing the institution that the particular person is no longer authorized is your only recourse.