If this is the plant you have, it's an Odontobrassia (Odbrs.) Kenneth Bivin. It's a cross of an Ondontoglossum and a Brassia (aka, spider orchid) and comes under the Oncidium Alliance. Phals sometimes rebloom on a recent spike. Other genera can, as well, but are less common. Oncidiums don't. You'll just have to treat this guy lovingly and wait till next year.
For what it's worth, I purhcased my Odbrs. Kenneth Bivin in bloom with a single spike and the next year it put up two huge spikes! It grows like a weed.