For me, it's when the first string gets scratchy and I can no longer get a pure tone. I can live with dead basses (if I'm not performing, which I'm not these days), but I hate a scratchy first string.
And, dead basses can be resurrected to a certain extent by tuning them down a 5th, pulling at them, and tuning them back up.
Amateurs practice until we get it right; professionals practice until they no longer get it wrong.
1999 Dake Traphagen (spruce);
2008 Dake Traphagen (spruce, double top);
2010 David Pace (cedar, double top);