Most certainly, when you go to replicate something, and fail, your first assumption is that you did something wrong. Even the second or third time. But after enough tries, you start to look for another explanation. "Irreproducibility", as Nature and the common scientist would use the term, doesn't mean "I tried once and failed", it means "I tried everything I could possibly think of and it still doesn't work".
Also, for many types of experiment it is questionable whether they are reproducible even in principle. One of the common analyses I do is called RNA-seq. It quantifies, for each of ~25K genes, whether and how much it went up or down with a given perturbation.
So the result of such an experiment is a 25K long list with numbers attached to each gene. What would it mean to replicate such a result? Surely the list of significant genes and pathways will not be identical even if a robot were to perform exactly the same experiment, due to biological variability.
Some people find this property of nonfalsifiability to be convenient, however...