He was still young enough to make at least two more Bond films.
There are two main reasons why Eon did not ask him to direct a fifth Bond film.
The franchise needed a new direction.
Brosnan's fourth and final Bond film, "Die Another Day, " was a financial success, but critics and fans complained that the series had become too drawn out. No one goes to a James Bond film expecting gritty realism, but parasailing on a CGI tsunami is definitely a step (or two) too far. Not to mention the ice palaces, invisible cars, and whatever else happened in the tedious finale.
Enter The Bourne Identity . Its down-to-earth fight sequences and stunts thrilled audiences more than Bond had in many years. I remember hearing several people say, "That's what James Bond should be like."
Even Brosnan
that something had changed after he saw the film.
It wasn't the first time Eon (the Bond producers) felt the need to take a different direction despite the financial success. Moonraker was a hit, though it was criticized for its over-the-top nature (James Bond in space!). The result was For Your Eyes Only , a more traditional spy film (and the first in some time to be based on Ian Fleming's material).
Eon did not drop Roger Moore for a new Bond film after Moonraker, but another factor was at play in the early 2000s:
Brosnan's price tag.
Brosnan earned $16.5 million for Die Another Day , and it's safe to assume he wouldn't want to take a step back for a fifth installment. Given this, hiring a different Bond would help steer the franchise in a new direction AND save millions of dollars upfront.
Craig earned $3.2 million for Casino Royale , the franchise was creatively rejuvenated and experienced a financial upswing, culminating in Skyfall , which achieved Avengers-level box office success.
I really like Pierce Brosnan and wish he could have made better Bond films, but there's no arguing about success.