Influenza neuraminidase (NA) is a sialidase that contributes to viral mobility by removing the extracellular receptors for the haemagglutinin (HA) glycoprotein. However, it remains unclear why influenza NAs evolved to function as Ca2+-dependent tetramers that display variable stability. Here, we show that the Ca2+ ion located at the centre of the NA tetramer is a major stability determinant, as this Ca2+ ion is required for catalysis and its binding affinity varies between NAs. By examining NAs from 2009 pandemic-like H1N1 viruses, we traced the affinity variation to local substitutions that cause residues in the central Ca2+-binding pocket to reposition. A temporal analysis revealed that these local substitutions predictably alter the stability of the 2009 pandemic-like NAs and contribute to the tendency for the stability to vary up and down over time. In addition to the changes in stability, the structural plasticity of NA was also shown to support the formation of heterotetramers, which creates a mechanism for NA to obtain hybrid properties and propagate suboptimal mutants. Together, these results demonstrate how the structural restrictions for activity provide influenza NA with several mechanisms for adaptation and diversification.