We consider a generalisation of abstract argumentation frameworks where arguments need to be backed by pieces of evidence in order to be actually present in the argumentation framework. These pieces of evidence come with an associated cost for retrieval and may not be available at any given time. We model an information-seeking agent in this scenario that aims at deciding whether a certain argument is acceptable while minimising the total evidence retrieval cost. We investigate the computational complexity of decision variants of this optimisation problem and find that, depending on the underlying classical argumentation semantics, complexity rises one level in the polynomial hierarchy compared to the classical case.