Here’s a clue:
Before you ask someone for a LinkedIn recommendation, scroll down to the bottom of their profile.
See the part where it says, “Interested In” and then a bunch of stuff like career opportunities, getting back in touch, and so forth? That’s important. Read that carefully.
If you don’t see “Reference Requests” as one of the things the person is “Interested In,” it means they’re not open to receiving reference requests via LinkedIn. They specifically went to the trouble of unchecking that box. Not everyone participates in stuff like that. It’s a free country.
So you definitely shouldn’t request a reference from that person six times. In fact, if you’re requested a reference six times from anyone, and they haven’t provided it, it means they’re not going to recommend you.