The Nikkei stock index fell for a sixth consecutive day Tuesday, giving up earlier gains as investors became cautious ahead of several key political and economic events in the United States, including a presidential debate. The 225-issue Nikkei Stock Average ended down 56.59 points, or 0.16 percent, from Monday at 36,159.16. The broader Topix index finished 3.19 points, or 0.12 percent, lower at 2,576.54. On the top-tier Prime Market, decliners were led by pharmaceutical, marine transportation and precision instrument issues. The U.S. dollar briefly climbed to the mid-143 yen zone in Tokyo on …