As I understand it, there are some fan-based and fan-supported, non-RPGA "Living", Living games and campaigns out there being run at various cons. If Living Traveller was not officially adopted by the RPGA, it could still be done.
The problem, as already posted, is coming up with a ruleset. The fact that different people play different versions and interpretations of Traveller shouldn't be a hindrance. Most D&D players play different interpretations of Greyhawk and the Forgotten Realms, as the previous posts on this thread suggest. People participating in the Living campaign would just have to understand that, for the campaign, everyone has to go along with the interpretation set down in the ruleset.
Finding someone or a group of someones to create that ruleset -- that's the biggest obstacle.
I would like to see the rules of the now-defunct Living Dragonstar campaign the RPGA used to run in order to see how they handled things such as characters getting together in different parts of the universe. I could see a real problem if, say, a Living Traveller player went to a con and participated in an adventure set in the Spinward Marches, then the next month went to a con and wanted to play the same character in an adventure set in the Linkworlds Cluster over in Ley Sector.
You would probably have to keep everything limited to one sector, or quadrant, or even a subsector. But still, you could run into problems keeping everyone's characters believably sychronized.
Although, now that I think about it, Living Greyhawk does a pretty good job of it. At the start of each of our years, it is another year in Greyhawk. Each charcter has 52 time units to use each year. Each adventure costs a certain number of time units. Other activities, such as Crafting items, use time units. You can't spend more than 52 time units in a (real) calendar year. Yet during that year, your character can go all over Greyhawk.
Hmmm. This might be doable after all. If we had a ruleset.