When the SS-Rank upgrade for the Karma Element started, William had already collected almost two dozen Severed Karma Threads. In comparison, triple that number of threads had snapped but some didn't produce a thread of their own.
William's body was incredibly weak at this point, and he needed some time to recover from the period of weakness before upgrading the Karma Element any more. According to the System, this would take anywhere from three to eight days, depending on whether William had to fight again during the time frame.
That said, William now had the required material to Ascend his Resist Karma Talent, which he started immediately. There was no reason to hold back on William's resistances, since they were key to surviving the dangerous Talent upgrades.