The pair needed to make the top 25 over the four tournaments to regain their card, and had done so before, after earning their cards from the same position last year.
However, neither looked likely at any point throughout the four events. Wilkinson opened the quartet with a tie for 47th, before missing the next three cuts, while Alker missed the final two cuts after opening with shares of 63rd and 57th.
It ends a run of four successive seasons on the world's leading tour for 39-year-old Wilkinson, who has held full tour card on seven occasions.
