Ah, that's one of mine too.
I would rather die than allow someone to help me and I'm always puzzled whenever I'm asked for help by someone, typical thoughts are "how weak not to be able to deal with this and that themselves", "don't they feel ashamed of themselves?", "then what would they do if there were no one around for them?" - at least offline, so to speak. I really don't have any solutions for you.
Could it derive from pride? If so, maybe you could take small steps to let go of the pride. Maybe start bothering people about smaller things, ask for small and easy favours?