RNG is RNG. Sometimes it is your friend; sometimes it is most definitely not your friend. Human nature says you'll remember the bad more than the good.
I've run Sha of Gold ever week, almost invariably on multiple characters. I run Galleon any time I can (which, due to him preferring to spawn while I'm at work, is nowhere near as often - but is still multiple times on multiple characters). Up until LAST NIGHT, I had yet to win ANYTHING from him, even burning alts' coins on him. (Last night he dropped a beautiful helm for my alt brewmaster - so happy!)
I've had good and bad luck with LFR: my druid gets screwed week after week... but my monk does alright. (My 'lock no longer does LFR, because there's no longer a reason to.) Some weeks are better than others.
I've seen people in guild (often in a party to make it less painful dealing with PUGs) go multiple weeks on multiple characters without winning anything. I've also seen people in the guild get four pieces of loot from ToES LFR in one week on one character. So it goes.