(often + in/with) to go on resolutely or stubbornly in spite of opposition or warning
(often + with) to be insistent in the repetition or pressing of a question, opinion, etc
to continue to exist, esp past a usual, expected, or normal time
to continue
Rain is likely to persist throughout the night
persister noun
[early French persister from Latin persistere, from per- + sistere to take a stand, stand firm]