A pup would need to be severely liver compromised (close to death) to not give them. Because if your pup does get heartworm, treatment of choice is Immiticide therapy (arsenic compound injections). At the least, slow kill with Heartgard would be done (which is rarely recommended). Unless the vet has said it's too risky, it's very important to give it.
BTW, my dog is liver compromised also.
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