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The 10 Downing Street site published the incriminating dossier on 4 October and crashed after experiencing huge demand.
The site's editors posted an apology and replaced the bin Laden document with a text-only version.
Late on Friday afternoon the site was still experiencing problems with ultra-slow access and further crashes.
A Downing Street spokesman said: "The site is one of the only places in the world where this evidence can be seen. We are experiencing an unprecedented number of hits. The previous busiest time was just after the general election when we received seven million hits in seven days and we are several times busier than that at the moment."
The site team attempted to combat the problem by turning more documents into text-only versions.
"We regret the problems," the spokesman said. "But there is little than can be done about sudden surges in traffic, and we are working on it."