Learn Russian: Учитель никогда не теряет терпения.

This sentence uses the Genitive of negation. When a transitive verb is negated with не, its direct object often takes the Genitive case instead of the Accusative. This is especially common with abstract nouns like терпение (patience). If the teacher were losing patience (without negation), it would take the Accusative: учитель теряет терпение.

Why do we use both никогда and не?

Russian requires a double negative. When you use a negative pronoun or adverb like никогда (never), you must still put не (not) directly in front of the verb. While English simply says 'never loses', Russian essentially says 'never doesn't lose'.

Why use the imperfective verb теряет in this sentence?

We use the imperfective aspect because this is a constant, habitual fact. The word никогда (never) shows that we are talking about a general state of affairs across all of time, rather than a single, completed event (which would require a perfective verb).

How do I form the Genitive ending for a word like терпения?

The dictionary form is терпение (patience), which is a neuter noun ending in -ие. To form the Genitive case for neuter nouns with this ending, you change the final -е to -я, resulting in терпения.