In "Half a Life," Dr. Timicin (played by the fantastic actor David Ogden Stiers) tries to help save Kaelon II, his homeworld. On the Enterprise, he works with Data and Geordi.
The Kaelons have a law on their world that once a person reaches the age of 60, he or she must be put to death. Once Dr. Timicin nears this age, the Kaelons no longer accept additional research/work from him. His work is of utmost importance, of course.
I believe it's stated in the episode that Timicin is to be "wined and dined" for a few hours/days before he's executed. I assume the latter, since the Kaelons are sure insistent that Timicin beam down to the world, apparently a few days before he turns 60.
I suppose that's the reason that they don't want Timicin to continue working on the ship: the festivities need to begin on the planet ASAP. However, why wasn't his work accepted? He wasn't yet 60 when he attempted to send new information to the Kaelon officials. You'd think that they'd gladly accept Timicin's work up until he turned 59.99999999999999999999... years old, not start to refuse it at an arbitrary time before he turned 60.