Canadian Raonic is one of six players going for the four remaining spots in London, but he is the outsider of the group and Friday's 7-6 (7/3) 6-3 loss certainly does not help.
In the last four, Frenchman Paire will face seventh seed Grigor Dimitrov, who defeated Kenny De Schepper 6-4 6-2.
The Bulgarian is playing in his first tournament under the guidance of new coach Roger Rasheed and is through to his first semi-final since July.
Top seed David Ferrer was given a walkover when fellow Spaniard Fernando Verdasco pulled out because of an abdominal muscle strain.
He next meets fifth seed Ernests Gulbis, who knocked out third seed Jerzy Janowicz 7-5 4-6 6-3.