Seller claimed final offer?

[Jennifer Cheu]

Hi BP community,

I am in the midst of buying a 3 family property, the list price is $440.  My initial offer on the house was at $420k, which was beat by an above list offer.  Lucky for me, the offer from the other party fell through, and I am now the only party involved in this discussion with the seller. 

After waiting almost a week, my buying agent tells me that seller came back with a final offer of $435k.  No option to counter.  Is that acceptable for them to do??  I had less than 24 hours to accept, and I did not see a formal counter in writing.  Is this common??