From the Unofficial Robotech Reference Guide:

From Robotech II: The Sentinels RPG:

About the Super Dimension Fortress Three: Pioneer
In 2014, the SDF-2 was completed, and placed under the command of SDF-1's first officer, Lisa Hayes. It's mission was to seek out homeworld of the Robotech Masters, Tirol, and to make peace with them, thus preventing a second Robotech War.
According to some sources, the SDF-2 was docked to the back of the SDF-1 for a transfer of parts, and other sources say it was still docked on the moon.
But all sources say that it was destroyed shortly before the SDF-1 was destroyed by Khyron in a suicide attack.
Even though the SDF-2 was destroyed, and most of the Earth's military command was decimated in that attack, the mission survived.
The construction of the SDF-3 started soon after a new defense command was formed, and like the SDF-2 before it, it was placed under the command of Lisa Hayes.
After nearly 7 years of construction, it was completed, and launched the day after the wedding of Admiral Lisa Hayes, the SDF-3's captain, and Major General Richard Hunter, the commander of the SDF-3's military forces.
It eventually found Tirol, only to discover that the Robotech Masters had already left for Earth, and the world was now in the posession of the Invid Regent.
An attack by the Invid left the SDF-3 crippled, but the United Earth Expeditionary Forces defeated the forces, and begun the repairs on the SDF-3.
During the time the SDF-3 was being repaired, a number of the SDF-3's command staff joined in the Sentinels Mission, and Tirol was placed under the command of Col. TR Edwards.
Near the end of the Sentinels Mission, a surprise attack by the Invid Regent once again crippled the SDF-3, but it was repaired, and upgraded, at Space Station Liberty.
After the defeat of the Invid Regent, the bulk of the UEEF fleet left on a new mission to liberate the Earth from the Invid while the SDF-3 folded to a barren world to test the Neutron-S Missile.
SPOILER: The test of the Neutron-S Missile completely decimated the planet, transforming it into a black hole, and trapping the SDF-3 within it's gravity. A ship from UEEF fleet did arrive to aid the SDF-3, but it was forced to retreat back to the main fleet to warn the SDF-4 not to use the Neutron-S Missile. END SPOILER
It's current whereabouts are unknown.