Really interesting thread. It's got me thinking a lot.
I'm quite introverted and prefer meeting with friends on a 1:1 basis or small group only, feel uncomfortable in large groups. I begged my bridesmaid not to ask too many people to my hen do as I wouldn't have enjoyed it.
My closest friends are a few from school, as we know each other inside out and can chat about anything. We only meet up maybe once every 2 months, but that's ok with me, life is so busy just with everyday family stuff that I dont 'miss' seeing them more often.
Other close friends (I only have a few I class this way, who I could share and trust secrets with etc) I meet every 6-8 weeks for lunch or dinner in a pub just 1:1. Strangely enough, these are former colleagues from different jobs that I somehow kept in touch with and get on far better with now that when we worked together, and we have more to talk about now we work in different places.
I have made a few friends at a baby group, we were all new the same week so got chatting and meet up socially occasionally.
This might sound horrible, but with having young DCs now and a fairly set routine with their activities, working pt (but still stressful on non working days), being close to family and seeing them regularly, means I'm probably quite closed to actively making new friends as don't know when I'd find time to dedicate to them. Although saying that, if I got chatting to someone say at one of the DCs activities and we got on really well I'm sure I'd make the exception.
Sorry that's probably not very helpful to you OP, just sharing my own perspective about why some people might not seem very forthcoming with invitations to meet up or start new friendships- they are probably struggling to juggle the plates in their life already.