I signed up with 3 last November on their Refer A Friend scheme,
whereby the referrer and the new customer each get £30 credit after 60
days.

When my credit didn't come through, I phoned 3, gave them the relevant
details and next day received a text saying the Refer a Friend had
been approved and I should see it on my next bill. I haven't had my
next bill yet, but when the referrer got their bill, again no credit.
They also phoned 3 and went through the same process, the next day
receiving a confirmation text.

Has anyone else had the same experience? Are 3 intentionally waiting
for people to chase the credit up in the hope that a (large)
percentage will just forget?

You are dealing with '3' - what do you expect.

You have probably lost a friend too :-(