Like most early Indian trading firms operating in South Africa, Dada Abullah & Co. went into rapid decline after the turn of the century.[1] The firm's founder and principal partner, Abdullah Haji Adam Jhaveri (i.e. Dada Abdullah) did not have any sons to succeed him, while his sole daughter was married in India. Thus, upon his death in 1912, the firm appears to have been dissolved.[2] This obviously long predates both the Second World War and the Great Depression.
Background:
Abullah & Co was one of the biggest South African trading concerns during the 1890s. At one point the company operated 15 branches and imported from Germany, India, and England. However, there were tensions between Dada Abdullah and his cousin Tayob Haji Hkan Mahomed, who managed the company's Transvaal branches. In 1890, Tayob bought out the firm's Transvaal operations and incorporated them as Tayob Hajee Abdulla & Co., but then fell short on the payments. The ensuing legal dispute led to Mahatma Gandhi's employment by Dada Abdulla.
References:
[1] Vahed, Goolam. "Passengers, Partnerships, and Promissory Notes: Gujarati Traders in Colonial Natal, 1870-1920." The International Journal of African Historical Studies (2005): 449-479.
[2] Padayachee, Vishnu, and Robert Morrell. "Indian Merchants and Dukawallahs in the Natal Economy, c. 1875–1914." Journal of Southern African Studies 17.1 (1991): 71-102.