Is the issuer liable?
Notwithstanding @JBently's detailed answer, it may depend on the terms and conditions the consumer agreed to when setting up the alert service - which may be additional or supplementary to the original card holder's agreement.
Using a random UK bank's alerts' T&Cs as an example:
We will not be liable to you if we do withdraw this ...
You don't necessarily need to turn to tort law to find a duty of care. For example, assuming the customer is a consumer (i.e. not operating as part of their business) then the following sections of the Consumer Rights Act 2015 are relevant:
49 (1) Every contract to supply a service is to be treated as
including a term that ...