Learn Russian: Они не хотят ни сдаваться, ни искать компромисс. - They want neither to give up nor to look for a compromise.

In Russian, ни ... ни doesn't negate the main verb by itself. You must create a double negative by adding не to the verb. So literally, the sentence says 'They do not want neither to give up, nor to look for a compromise.'

Why is there a comma before the second ни?

Russian punctuation rules require a comma before the second part of a double conjunction. Whenever you use repeating pairs like ни ... ни, и ... и, or или ... или to connect items in a list, you must place a comma before the second word in the pair.

Компромисс is the direct object of the verb искать (to look for). Why doesn't its ending change to show the accusative case?

It actually is in the accusative case! Because компромисс is an inanimate masculine noun, its accusative form is exactly the same as its dictionary (nominative) form.

Why does сдаваться (to give up) end with the reflexive particle -ся?

The non-reflexive base verb сдавать means 'to hand in' (like an exam) or 'to rent out' (like an apartment). Adding the reflexive -ся changes the meaning to 'to surrender' or 'to give up' — you can think of it as handing yourself in.