You should use rbind
instead of grid.arrange,
plots <- list(p_a, p_b, p_c)
grobs <- lapply(plots, ggplotGrob)
# for gridExtra < v2.3, use do.call(gridExtra::rbind.gtable, grobs)
# for gridExtra >= v2.3 use:
g <- do.call(gridExtra::gtable_rbind, grobs)
library(grid)
grid.newpage()
grid.draw(g)