How do you build a small daily habit that survives a bad week?

Design it for your worst day rather than your best. That usually means shrinking it until it takes under two minutes, attaching it to something that already happens reliably, and defining a reduced version that still counts. The failure mode is not missing once; it is missing twice, so the rule that matters most is never skipping two in a row. Track it somewhere visible, because the record itself becomes motivating. Expect that the habit will feel pointless while it is small — the size is what makes it survive the weeks that would otherwise end it.