By Mari Saito, Aaron Sheldrick and Kentaro Hamada TOKYO (Reuters) - Three years after the Fukushima disaster prompted the closure of all Japan's nuclear reactors, Prime Minister Shinzo Abe is moving to revive nuclear power as a core part of the energy mix, but many of those idled reactors will never come back online. This means Japan is likely to remain heavily reliant on imported fuel to power the world's third-largest economy, straining a trade balance that has been in the red for nearly two years. Hokkaido Electric Power Co and Kyushu Electric Power Co, both facing a third year of financial losses, are seeking capital infusions totaling nearly $1.5 billion from a state-owned lender. Fukushima operator Tokyo Electric Power Co was bailed out by the government after the March 2011 disaster.