The Football Association decision means Altrincham will be relegated to the Conference North.
It follows a ruling that they should lose all the points gained while midfielder James Robinson, who did not have international clearance, played.
Scarborough are likely to benefit and be reinstated to the Conference.
A statement from the FA read: "At an Appeal Board hearing today, Altrincham FC's appeal against a disciplinary decision by the Football Conference was rejected.
"Altrincham were deducted 18 points and fined £1,000 by the Conference in April for fielding an ineligible player, James Robinson.
"The sanction was based on the points won by the club in the 13 matches Robinson played. This sanction was upheld by the appeal board today.
"The appeal board therefore had no option but to reject the appeal as Football Conference rules do not allow discretion on the matter of sanctions for specific breaches of rules."
Altrincham, who signed Robinson from Accrington after a spell in Iceland, claimed the deduction was unfair.
But three members of the FA's sanctions and regulations committee turned down the appeal.
Scarborough, who finished bottom of the Conference, will only be reprieved if they are able to assure the Conference board that they are in a sound financial position after coming out of administration last week.
Tamworth, who finished the season second bottom, have already been reinstated following Canvey Island's decision to withdraw from the Conference.
An Altrincham statement said: "After the FA today upheld the Conference's earlier decision, the Altrincham FC Board are deeply disappointed with today's decision by the FA Appeals Panel.
"After a successful season on the pitch, this decision has come as a complete shock.
"On the positive side, the management and Board are totally committed to take the club onwards and upwards on the foundations set over the last four years.
"We can but thank our own fans for their loyalty and also the supporters and clubs throughout the English football community for their support."