A paladin guildie grinded for 21k first week of the patch on AB weekend in about 16 hours. She wanted GM claymore badly but still... It's not something sane...
My highest is 9k at the first week, happily merrily AVing.
Most it one day is probably around 8k, but I have 4 at/near-60 chars, so it's spread between them. I've earned almost 40k honor and have only been able to buy 1 reward cause my points are so spread out.