Phaius
 

How do I get my phaius 'tropical ice' to rebloom?

Not enough info. You need to tell us how you're growing it.

How much light does it get? How often do you feed it?

There is no registered phaius hybrid named Tropical Ice, but phaius are typically shade- and warmth-loving creatures, and prefer to stay evenly moist and moderately fed pretty much throughout the year.

I think the correct name may be Phaius Dan Rosenberg "Tropical Ice".

I just looked it up. To be totally accurate and up-to-date, it's Gastrophaius Dan Rosenburg 'Tropic Ice' HCC/AOS.

It's a cross of Phaius tankervilleae x Gastrorchis tuberculosa (abbreviated Gp.), and the cultivar (note single quotes) was awarded!