In the true sense the unluckiest pair would be one that had a career ending injury (Paul Binnebose, for example), or missed a golden opportunity due to an injury, like Tai & Randy. However, I want to talk about a pair that did not have an injury, and yet they turned out to be very unlucky.
I was watching some of my old tapes this weekend and I happened to watch Shishkova-Naumov's LP (skated to Schubert's Unfinished Symphony) at the 1995 worlds. It was loaded with technical difficulty, and they delivered it. The only flaw was they finished a couple of seconds behind the music. Sandra Bezic's comment was (why do I even take her seriously?) - the audience isn't moved; technically it was flawless. I believed then, and I believe now that S&N should have won over Kovarikova-Novotny (I liked them too) who had a mistake on a sbs jump, and technically their program was not as demanding. It was close, but not in terms of the judges marks. S&N were really held down to leave room for K&N.
I noticed them for the first time at the 1992 Olympics. Loved their SP skated to 'Take Five'. I thought 1994 would be their year, but the pros returned- G&G and M&D. So S&N were pushed down. They lost a close decision for the bronze to Brasseur & Eisler because B&E were the reigning world champions (JMO- why they lost), so they did not even win an Olympic medal. That was very unlucky. They should have been contending for the OGM in 1994.
I used to like S&N. They were not comparable with other great Russian pairs like G&G, M&D, B&S (R&Z and P&P were another generation, IMO), but they were a very good pair. Shishkova had beautiful positions and pointed toes on the lifts, spirals and everything she did. Their jumps and throws were not always solid, but they were not horribly inconsistent either.
They were also unlucky in terms of ice time. During that time Russia did not have that many skating rinks, I think, and their practice time was limited to 2 hours a day.
IIRC after the 1996 worlds where they did not even medal, they turned pro. It looked like their fed was not supporting them. Even as pros it seemed like no matter how well they skated, they never got good marks from the judges.
I wish Shishkova-Naumov had had more success than they did. They did win a world championship, and a world silver, but they were good enough to win more.