You normally use this in situations where something keeps going wrong, again and again. Like; "I've had a date planned for the last week, but every day it has rained, if it's not one thing, it's another". Hope this helps. :)

Australians use this idiom a lot, because we either have droughts or floods. Example: How's your farm? Well you know, last year we had bush fires, this year we had a big flood. "If it's not one thing, it's another."