This is a topic that most medical students discuss at some point of time. I have found myself in the midst of similar conversations over my years at medical school.
After much study, I happened to reach an understanding that clarified the purpose of the test and provided a way to understand the results as well.
It would help if you think of the cerebellum as a processor (such as a C.P.U. in a computer).
There are 3 main inputs:

Romberg's test (3 steps):
1. Ask patient to stand with feet together.
2. Ask patient to close both eyes.
3. Maintain the posture for 60 seconds.
The Romberg's test is positive if the patient cannot stand for 60 seconds with feet together and eyes closed.
It is essential to understand that without the processor, the inputs do not matter (as there will be no output and no result).
Thus in Cerebellar ataxia, the patient will be unable to perform any of the above 3 steps and thus the Romberg's test cannot be performed on this patient.
In a situation where the cerebellar function is intact and Romberg's test is performed:
The first input (Vision) is lost when the eyes are closed.
It is now unto the 2 other pathways (Proprioceptive and Vestibular pathways) to provide input to the cerebellum.
Thus the Romberg's test will be positive in cases of:
1. Proprioceptive dysfunction e.g. Sensory peripheral neuropathy & Dorsal column dysfunction
2. Vestibular dysfunction e.g. Vestibular neuritis
This was my attempt to provide a brief summary about this topic and it has been compiled to the best of my understanding. Please feel free to discuss it further, in the comments section below.
Have a great day!
- Vikramjeet Kakade