The phrase "a severe setback when" is correct and usable in written English.
It can be used to describe a significant obstacle or difficulty that occurs at a specific time or under certain circumstances.
Example: "The project faced a severe setback when the funding was unexpectedly cut."
Alternatives: "a major obstacle when" or "a significant hindrance when".
Late last year, Mr. Wang had a severe setback when he fell off his bicycle during a delivery and shattered his arm.
Our diplomatic relations suffered a severe setback when our Embassy compounds in Tehran were overrun in 2011 and the Vienna Convention flouted, and when the Iranian Majles voted to downgrade relations with the UK.
Tentative and still fruitless efforts to lure the Taliban into a peace process were dealt a severe setback when a man claiming to be a peace envoy killed Burhanuddin Rabbani, the leader of Afghanistan's High Peace Council and a former president, using a bomb hidden in his turban.
They continued moving the ball forward on short rushes, but almost had a severe setback when Weiss fumbled during a carry.
Oakland's attempt to buy the Raiders football team and move it back from Los Angeles suffered a severe setback today when the California Supreme Court rejected the city's appeal to reinstate its suit.
The Action Française reached its apogee following World War I, when nationalist feeling was strong, but suffered a severe setback in 1926, when it was publicly condemned by the papacy.
China's Tibet strategy appeared to have suffered a severe setback earlier this month when the reincarnation of another important lama unexpectedly appeared in Dharmsala, India, the seat of the Tibetan government-in-exile.
Haiti's economy suffered a severe setback in January 2010 when a 7.0 magnitude earthquake destroyed much of its capital city, Port-au-Prince, and neighboring areas.
That fight suffered a severe setback on Monday when the Supreme Court denied to hear a lawsuit Evans filed against her former employer in April 2015, claiming that she was a victim of discrimination.
In March 2015, however, Vanuatu suffered a severe setback to its development when Cyclone Pam, a category 5 (highest intensity) tropical cyclone, struck the islands.
Japan's whaling program suffered a severe setback on 31 March 2014 when The Hague-based International Court of Justice (ICJ) found the lethal sampling was not justified "for purposes of scientific research".
