Q:

How do you destroy a battle standard?

AV states that Battle Standards have resist 50 all when deployed, but it says nothing about their total health. Can an enemy destroy them by picking them up out of the ground and breaking them in half?
If it breaks, how can it be repaired?

A:

There is nothing hard and fast specific to battle standards written in the 4e rules that I am aware of. However, the Rules Compendium(pp 176-177) (and I'm pretty sure the DMG (p65) has this as well) has a table for the very purpose of attacking objects.
Here is the table from the online compendium:
Object Size AC or Reflex    Fortitude   HP  Example
Tiny    10  5   5   Bottle, book
Small   8   8   10  Treasure chest, manacles
Medium  5   10  20  Door, statue
Large   4   12  40  Wagon, vault door
Huge    3   15  100 Big statue
Gargantuan  2   20  200 Even bigger statue 

In this case I'd probably go small or maybe medium. There is also a table for modifiers but they may or may not be relevant to trying to attack a battle standard.
Suffice to say you're looking at an AC/Ref of 5-8 a Fort of 8-10, immunity Will (as well as necrotic, poison and psychic) and HP between 10-20 (unless you choose to modify this with an HP multiplier, but that is up to you).

As far as restoring the standard after it is broken, the make whole ritual is provided for this very purpose. 
Make Whole
As you finish the ritual, the oaken door stands whole and unblemished as if Orten the Rager hadn’t just burst through it with murder in his eyes. It’s the least you can do after using the inn to ambush the infamous barbarian.
Component Cost: Special
Market Price: 50 gp
Key Skill: Arcana (no check)Level: 1
Category: Exploration
Time: 10 minutes
Duration: Permanent

A single object that can fit in a 10-foot cube is completely repaired. The component cost is 20 percent of the item’s cost. In cases where you attempt to repair an item not on any price list, the DM determines the cost.

