Can double-manned trailers run non-stop continuously?

No. Once both drivers have finished their 10 hour shifts then they must stop and take a break.

This is a legal requirement. The drivers mate MUST be in the passenger seat when not driving. So with 2 fresh drivers, they can drive for 20 consecutive hours before they both have to stop for a mandatory 9 hour break, then another set of 20 consecutive hours driving can be undertaken. Standard driving breaks every 4.5 hours are still required.