"despite success" is a perfectly valid phrase in written English.
It can be used to express the idea that even with success, there are still challenges to be overcome. For example: "Despite success in the polls, the candidate still faced a difficult battle to win the election."
Despite success in the tire division, Pirelli stock has fallen 57percentthis yearar.
Despite success abroad, the company has only a small broadcasting platform in the United States.
Despite success in the past, they remain mostly confined to morning and daytime slots.
But despite success stories like Dance Central and Kinectimals, owner frustration soon began to overshadow those rosy sales figures.
Here she explores her own spiritual crisis; despite success and a loving husband and son, "I had begun to quietly fall apart," she writes.
Despite success in capturing key leaders of Al Qaeda in recent months, he said, "They are still a very dangerous component and adversary".
Despite success setting up a school in the capital, Rakshand knew that the places in Bangladesh with the least opportunities for children were rural areas.
Despite success at every level, even a Heisman Trophy winner like Dayne must learn to trust his skills and his strength against National Football League defenses.
America's war in Afghanistan, despite success in driving Al Qaeda from its bases there, has yet to produce significant information about the planning and execution of the attacks.
That pragmatism may well have served Republicans better had they not selected such ideologically narrow candidates, who despite success in their respective primaries still went down to defeat on Election Day.
Despite success beyond anyone's expectations, Santorum finished the race in much the same place he started it: as a factional candidate unable to attract a broad spectrum of Republican voters.
