British production company Eon Productions has been around for, well, eons. It was started in 1952 by Albert Broccoli and Harry
Cauliflower Saltzman, and produced the first Bond film, Dr. No, in 1962 and every single Bond film since (except for a couple of weird offshoots, like a comedy version of Casino Royale in 1967).
After Dr. No proved to be a huge success, Eon knew they had to make another Bond film. They had nine Ian Fleming Bond novels to choose from. Which would they pick? The wrong choice could mean disaster. It was like playing Russian roulette with the man with the golden gun.
The choice was kinda made for them after President John F. Kennedy declared From Russia, with Love to be his favorite Ian Fleming novel (source). Eon went ahead with production on From Russia with Love. If it turns out bad, maybe the president could sign an executive order commanding the nation to see it.
He didn't need to.
The movie grossed almost $25 million. That more than paid Connery's $250,000 salary, a whopping 14-times increase from his Dr. No payday (source). It was definitely another smash, or should we say SMERSH, hit.
The Broccoli kids started helping with production in 1972 and continued in their father's footsteps, producing Bond films right up through Skyfall and SPECTRE. Eon has branched out into a few non-Bond films, but 007 has been their bread and butter—or maybe scones and jam—since 1962 (source). And if it ain't broke, don't fix it.