Strong admissibility plays an important role in formal argumentation under the grounded semantics, especially when explaining the acceptance of an argument. However, strong admissibility has so far only been defined in the context of finite argumentation frameworks. In the current paper, we examine the case of infinite argumentation frameworks. In particular, we assess what the challenges are when moving from finite to infinite argumentation frameworks and we show that despite these challenges, strong admissibility can be meaningfully defined and applied in the context of finitary argumentation frameworks.