Collocations for persistent - adj.

be

extremely, incredibly, really, remarkably, very
The weeds were very persistent.

stubbornly
a stubbornly persistent unemployment problem

quite, rather
Some infections can be quite persistent.

Persistent is used with these nouns:
cough, critic, diarrhoea, drizzle, failure, fever, myth, offender, pain, problem, rain, refusal, rumour, truancy, truant