The solution I've gone with is based on the first comment from @docendodiscimus

Rather than attempt to create a new data frame as I'd been doing this approach simply adds columns to the existing data frame by taking advantage of dplyr's mutate() function.

My code is now...

df %>%
  group_by(variable) %>%
    arrange(variable, event.date) %>%
      mutate(ip.value = na.approx(value, maxgap = 4, rule = 2))

The maxgap allows upto four consecutive NA's, whilst the rule option allows extrapolation into the flanking time points.