Oxford University researchers report two cases of patients in Vietnam who died after failing to respond to treatment with the drug.
Details are published in the New England Journal of Medicine.
The H5N1 variant of the bird flu virus has so far killed 71 people in south east Asia.
Experts fear the virus will mutate and gain the ability to pass easily from human to human, which could trigger a global flu pandemic.
The lead researcher in a study listed in the journal Nature, Dr Jeremy Farrar, is becoming concerned about the mutation.
"We don't have a back-up at the moment, so we can't combine it with another drug, as we would with HIV, to prevent drug resistance developing."
