Use 'importune' to show the person being asked is likely to be annoyed or troubled by the persistent requests. She began to importune her brother, daily demanding he fix her laptop.
Pro Tip 2/3
Persistence Implied
The word captures not just asking but doing so repeatedly over a period of time. His friends continued to importune him for a ride despite his initial refusal.
Pro Tip 3/3
Inconvenience Highlighted
'Importune' often suggests the request may be at an inconvenient time or place. He would importune her for a loan, even during her busiest hours at work.