。
She'd grown sick of his persistence.
Literal
She [topic-は] his [genitive-の] persistence [at-に] was-fed-up.
うんざりする ('be fed up, sick of, weary of') is a 擬態語 + する construction — うんざり is a state mimetic for the feeling of being thoroughly tired of something, then converted to a verb with する. Source of the weariness takes に. 執拗さ is the noun form of 執拗 (しつよう, 'persistent, tenacious') via the ~さ nominalizer; 執拗 itself is a Sino-Japanese na-adjective often used for unpleasant doggedness (like a pestering ex or repeated rumors).