In 1930 he was the runner-up for the Japanese championships, which he finally did win the next year. Also in 1930 he was a runner-up for the Mid-Pacific Invitational tournament losing to American Cranston Holman and the doubles final as well.
In 1931 he lost the Miramar L. T. C. title in Juan-les-Pins against his brother Hyotare Sato, won the doubles, and was a finalist in mixed doubles. He clinched the West-England Championship in singles and doubles. He was defeated by Jean Borotra for the British Covered Court Championships title. He partnered his brother to gain the Beau Site Club de Cannes second meeting trophy  and the St. RaphaĂ«l T.C. title. In singles competition he claimed the Country Club de Monte-Carlo second meeting title (the same tournament in which the Sato brothers reached the doubles final). He became Dutch doubles champion alongside Minoru Kawachi. In July he beat Vernon Kirby for the Tunbridge Wells Championship. He captured the Midland Counties Championships in singles and mixed doubles the same month and only losing the doubles final.
Sato played with a flat forehand drive which he modeled after Henri Cochet when Cochet visited Japan in 1929. He hit the ball on the forehand side early after the bounce and he was an excellent volleyer.
On April 4, 1934, Jiro Sato was on the ship N.Y.K. Hakone Maru crossing the Strait of Malacca to Europe for a Davis Cup match against the Australia Davis Cup team in the second round of the 1934 International Lawn Tennis Challenge. Earlier in the day he complained of stomach pains and thus had no appetite and kept to his cabin. He considered leaving the ship at Singapore, which he did for a medical examination. The exam revealed no reasons for his health problems and it was concluded that his problems were psychological. Sato was nervous and feared that his illness would be an obstacle for his team to win. As the day passed, the Japan Davis Cup team was given a banquet hosted by the Japanese consul to Singapore. Sato was present and was further pushed by the consul and his teammates to proceed with the trip and sail to Europe. That same day a cable was received from the Japanese Lawn Tennis Association insisting on Sato's participation in the Davis Cup and that the voyage should be resumed without delay.
At 11:30 p.m. on April 5, 1934, before reaching Penang, Sato was found missing by his compatriot Jiro Yamagishi. The last time he was seen was at 8:30 p.m. when he had dinner in his cabin. He left two suicide notes, one to his Japanese tennis teammates expressing doubts that he would be able to help the team in the upcoming contest. He begged them to forgive him and do their best to prevail in the match. He promised he would be with his colleagues in spirit. The other note was addressed to the ship's captain, apologizing for the inconveniences that his actions might cause. A search for him continued for seven more hours and the vessel hovered in the strait. Wireless messages were sent to nearby ships. Later further evidence was found which confirmed the suicide theory. Two iron davit-winding handles and a training skip-rope were missing, which Sato probably used to tie weights on himself to make sure he would drown. After discovery of the new evidence, the ship sent out a radio message stating that "Japan's finest tennis player and national hero was believed to have committed suicide by throwing himself overboard". On April 6, a prayer was ministered by his friends who assembled on the deck of the ship. An altar was built on board with photographs and racquets of Sato around it. Also a traditional Japanese "cake offering" ceremony was held. It was speculated that the pressure on him came from the growing prestige of the Japanese Empire and from the Japanese Lawn Tennis Association who refused to allow the exhausted Sato to have a break from tennis and skip the 1934 season. He became depressed and concerned about his abilities.