The Ultimatum Approach
Presenting your counter-offer as the final offer isn't appropriate. Present your counter-offers and consider their offers without ultimatums. Decide on whether the offer on the table is acceptable, only after you have walked away and used some time to think. Negotiation is the art of exploring mutually beneficial possibilities, instead of issuing ultimatums.
Continually pointing out what is wrong with the offer on the table is not particularly pleasant for the other party. They are trying to find a solution, while you are constantly looking for what's wrong.
Talking Too Much
Some would say that the "winner" of any negotiation is the one who talks less. Be succinct and reasonable in presenting your views, and listen carefully. Don't ramble on and don't repeat yourself.
Falling in Love with One Element of Compensation
Focusing exclusively on one component of the compensation could be a kiss of death, particularly if the employer is severely constrained on that dimension; for example, "Less than 1% equity in the company is unacceptable."
"I can find anywhere at least $50,000 more than what you are offering." If that is the case, why are you negotiating? Time to go to where you can find that kind of money!