What did your Realtor say?
If you are making an offer under asking price, did your Realtor substantiate the price you are offering, or is it just a low ball offer?
I am a big believer in getting the best price, and if your Realtor could add something additional to your next counter, such as market stats, it would not simply you asking for a lower price.
Did your Realtor talk with the other broker? It is very common for top Realtors to discuss why the seller is selling, how much they want or need to net. This question sounds to me as though that type of conversation is not happening. And if this is their second counter, and this time it's "firm", then if I were your Realtor I would want to know more information.
Normally before I submit an offer I talk with the listing agent and find out what is important to them. Net price, why they are selling, timing, length of escrow, preferred title and escrow, etc. By establishing a good relationship with the listing agent, the two agents actually try to help both parties work to a common agreement of price and terms that both parties perceive as "win -win'. It is the best way to do business.