Use the verb persevere when you want to persist in anything and continue despite difficulties or obstacles.
The verb persevere comes from the Latin root persevereus which means "continue steadfastly, persist" and that word comes from two others, per- for "very" and severus for "strict." So, today, the connotation of the word is to persist in a methodical way despite obstacles or distractions. You can see the relationship between persevere and perseverate, which means "to persistently repeat something," and that word is a medical term used to describe stuttering.
v be persistent, refuse to stop
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ask for it, ask for trouble
persist with actions or an attitude despite the probability that it will cause trouble
plug, plug away
persist in working hard
follow, stick to, stick with