丧失 is more formal and serious than 失去 (shīqù). Use 丧失 for abstract/important things: 丧失信心 (lose confidence), 丧失理智 (lose reason), 丧失能力 (lose ability). For everyday items, use 丢 or 失去.
grammar
丧 has two pronunciations: sàng (to lose) in 丧失, and sāng (mourning/funeral) in 丧事 (funeral matters).
