What does sine dominico non possumus mean?

It means "Without Sunday we cannot live"

In the 4th century, Roman Emperor Diocletian had made a decree that any Christians posessing Scripture, meeting to celebrate the Eucharist, or constructing any buildings that could be used for religious gatherings would be put to death.

In 304 A.D. a group of 49 Christians from Abitene (present-day Tunisia) were taken captive by the Roman Empire for meeting privately to receive the Eucharist. When asked by their prosecutors why they would do something so foolish they responded "Sine dominico non possumus" translated - "Without Sunday we cannot live. "