He was in an accident
Wikipedia explains that:
However, he was ultimately unable to appear [in Episode II] due to a motorcycle injury
This is confirmed in an ABC News article from the time, which details that:
The Oscar-nominated Irish actor suffered a fractured right pelvis, a
chipped left pelvis, and multiple leg abrasions.
Apparently the motor cycle accident happened about noon 11th July 2000 and, as Episode II: Attack of the Clones was released in 2002, it's fair to say that production would have started well before then, meaning that Neeson couldn't be involved due to the serious accident.
So that addresses why he couldn't be involved, but
something doesn't quite add up...
The production of Episode II began before the accident:
After the mixed critical response to The Phantom Menace, Lucas was
hesitant to return to the writing desk. In March 2000, just three
months before the start of principal photography, Lucas finally
completed his rough draft for Episode II. ...The final script was
completed just one week before the start of principal photography.
... Principal photography occurred between June 26, 2000 and September 20, 2000 at 20th Century Fox Studios in Australia.
So, the final script was not completed until about 19th of June 2000. Yet, Neeson's accident occurred after that date!
Even more evidence about something else being involved is this later draft, which was last modified July 5, indicating that Neeson wasn't going to be involved - Qui-Gon is only mentioned, not actually involved!
Now, just to confirm that Neeson wasn't involved, although Wookieepedia correctly says that in Episode II:
Back at Coruscant, Yoda senses a terrible darkness in the Force as the slaughter continues (Qui-Gon Jinn's voice can also be heard saying "Anakin, Anakin, No!" during this scene)
IMDB explains that this was archive sound
Now, this article indicates that Neeson was very unimpressed with Episode II.
So, perhaps he couldn't be involved because of the motorbike accident, but maybe he didn't even want to be involved.
As for Episode Three, Neeson was involved, just not in the final version (kudos Praxis):
Liam Neeson has said that he recorded a cameo as Qui-Gonn Jinn, which
was to feature in a scene with Yoda, further explaining the concept of
a Jedi communicating from beyond the grave. In the script, the dialog
(in which Qui-Gonn is heard, not seen) appeared in the scene in which
Yoda is meditating on the secret asteroid base, just before Bail
Organa informs him of Obi-Wan's return with Padme. The scene does not
appear in the deleted scenes section of the DVD, however an unfinished
version was included in the Blu Ray Release Box Set.