Step 1: Classify conjunctivitis by tempo. "Severe" here is the keyword for the hyperacute presentation, which has the most copious discharge and the fastest course.
Step 2: Among bacteria, only the Neisseria species ($Neisseria\ gonorrhoeae$ and $N.\ meningitidis$) cause this hyperacute picture, typically in neonates (ophthalmia neonatorum) or sexually active adults exposed to genital secretions.
Step 3: The danger is corneal: gonococcus can invade an intact cornea, so untreated cases risk ulcerative keratitis and perforation. That is why it is graded as the severe form.
Step 4: The remaining options - $Staphylococcus$, $Streptococcus$ and $Haemophilus$ - drive the run-of-the-mill acute conjunctivitis, which is benign and not labelled severe. Eliminating them leaves Neisseria.
\[\boxed{\text{Neisseria}}\]