Is it possible to go deaf at a random time?

A lot of reasons: most commonly is just having an intermittantly congested ear (pressure differences between the inner and outer.. ear poppping). Water/wax other obstructions. There can be a sudden problem with the auditory nerve (always ONE side)... and quite rare compared to the other causes.

Yes: An autoimmune disorder can cause deafness although this is a rare cause. Certain medications have also caused deafness through toxicity. These situations show more rapid onset deafness rather than the more common gradually developing hearing loss which may be genetic or degenerative.