Hello Helen
Let me clarify. Take a look at the topology of the lab:
SW1 and SW2 can communicate with each other over their Gi0/1 interfaces in order to determine the AVG, and the AVF. Even if the links towards R3 fail, this link remains active.
The role of the AVF is affected directly by any failure in the uplinks to R3. If Gi0/2 goes down on SW1 for example, SW1 can no longer play the role of the AVF.
However, Unlike the AVF, the role of the AVG doesn’t require this link to R3 be active. So SW1 can remain the AVG, even if its Gi0/1 link goes down. The only failure that will cause another switch to take over the role of AVG is if the switch itself fails (power outage, corrupted IOS, the GLBP process fails) or if the Gi0/1 interface fails and communication with SW1 is lost.
Actually, if two links to the router fail, the AVG priority will not change. However, the weight which determines the AVF will change.
I hope this has been helpful!
Laz