What happens when the border router resets? Is it required for all the devices (sensor motes and routers) be reset to rejoin the network?
The border routers are typically mains powered and care must be taken to ensure there is no power outage to maintain seamless connectivity.
However, in some cases it is possible that the border router may have to be reset or power cycled; in such cases, in a 6LoWPAN network, the devices (nodes & routers) need not be physically reset.
As per the 6LoWPAN protocol, all the devices in the network initiate rejoin procedure. This is the good news is performed automatically by using DAO Trigger Sequence Number (DTSN field, part of the DIO message) that is transmitted. This field is part of the mechanism that is provided to trigger DAO messages. The border router stores this DTSN in flash memory area and when the Border Router (BR) is reset, it increments this value before triggering the DIO transmission.
All the devices (sensor motes, routers) keep track of the DTSN that it has heard from the last DIO from its "Parent". When any node receives a DIO with newly incremented DTSN, it triggers the rejoining procedure. When the routers receive a DIO from border router with incremented DTSN, they increment their own DTSN before triggering the rejoin procedure.