The imprecision could be fixed by forbidding the first digit from being 1, switching to a lower unit instead. So up to 120 seconds ago, then up to 120 minutes ago, then up to 48 hours ago, then up to ~61 days ago (ick, months are evil), then up to 24 months ago.

When such relative dates are in a list it's generally tolerable. The failure to update is far more irritating, and limiting to "yesterday" does not fix that.