The Chinese government gets a bit upset if you say the "border" is closed.... because they believe Tibet is part of China, so there's no border as such. However, all foreign travel to the Tibet region needs a permit from the government, and from time to time they stop issuing permits. These periods usually coincide with anniversaries or events likely to be associated with Tibet independence or relating to statements by or actions of the Dalai Lama.
This will be the 5th year in a row that permits have been denied during this period, because it coincides with Tibetan new year (Feb 22-24) and the anniversary of a Tibetan anti-government uprising on March 14, 2008. about 8 years ago
The exact reopening date may not be 31 March 2012. Nothing can be certain and the reopening date is usually announced one day before the actual reopening, so if you plan to come around April, better come after the first week of April. Or have a contingency plan if you come within the first week of April. almost 8 years ago