"A Red, Red Rose" has time on its side. Scratch that. "A Red, Red Rose" blows time out of the water. Sure, the lovers may be apart for a while, but that's no matter because their love transcends time. It can practically survive an apocalypse, for crying out loud. The lesson here is that for Robert Burns, time is no object when it comes to great love.
The whole point of this poem is that love exists out of time. So growing old, being apart, and even dying have absolutely no effect on it.
The whole point of this poem is that we only live for a short period of time. The "sands o' life" pass quickly ("run"), and we should make the most of it.