Some people have a social "gift". They love being social, they are social, people are drawn to them, and they effortlessly collect lots of friends. I know some people like this. I don't have that gift. Most people don't. The average person has to work at being social. And some people have an extremely difficult time, especially if something is "off" or off-putting about them.
You seem perfectly nice. And you have lots of acquaintances, so you must not be off-putting. So you need to ask yourself when relationships have not progressed to the next level, is it because you tried to reach out in a meaningful way for more than just casual stuff but were rejected? Or did things just somehow not progress and you didn't know why the people were making other friends but your were excluded?
I have overcome this hurdle. I am a hermit by nature who used to have very few friends into my mid-thirties. Now at 43 I have LOTS of friends. AND I'm a very busy (overwhelmed) single mom of three young kids. I could EASILY be lost in the mommy vacuum of my comfy home too busy to deal with people. That would be my comfort zone. But I have learned that because I'm not a natural social magnet, I have to APPROACH and initiate relationships with people and I have to maintain them, and I have to not get miffed when I seem to be doing most of the work. It's not about cliques or popularity for me, I've learned community is important, especially with kids, and LOTS of nice people are out there, equally busy and with just as much trouble making friends.
Do my efforts sometimes go unnoticed while the more magically social people meet up and do stuff without me? SURE! but I don't mind, and I keep initiating other meetings, etc. And I don't have much time to socialize, but I can at least send a personal FB inquiry, or make a call, or make a visit, or ask someone to meet several times until it really happens. Over time, it has gotten more natural and once the relationship is established it becomes more mutual. I have learned lots of people just assume I'm too busy for them with kids and all, so I have to make a point of being available.
I have neighbors I am close to and ones I wouldn't know if I ran into them. ALL the ones I am close to are ones where I MADE IT A POINT TO APPROACH and be nice to them. I lingered in the yard and talked when I didn't feel like it. I asked for help from them. I left thank you gifts for helping me. I shoveled their walk when I shoveled mine. I raked their leaves when I raked mine. (They have since reciprocated many times) I smiled and waved and said hello rather than hiding... I walked over and introduced myself. No one came to my door and tried to meet me. I had to do it. This is naturally the way for most people.
There is a group of moms in the waiting room for my kids' taekwondo class 4 nights per week. They've always been friends since I started my kids there. They meet up for play dates and always sit together etc. They never invited me into their group. I don't know how they all got so close. But I nosed right in there. Sat with them, asked them questions. Asked questions about their kids. Paid attention to their kids' accomplishments in class so I could make genuine comments and cheered for them in tournaments. Facebook friended them, and now I'm one of their friends too. They didn't invite me though. So what? I'm used to not having the "gift" of easy magnetism, but I've also learned that being sincere and nice and brave goes a long way and almost no one rejects your efforts-I actually never have been rejected since I started making an effort. I also reach out to the quiet or new people in the waiting room even if it's a smile or to chat. Its not my nature, but I can certainly do it. I know all too well you can sit in that waiting room for months and none of those nice people will say anything to you if you're new. I do though.
I got one reminder along these lines from my VERY social friend a few years ago. I got her to join my gym which I had been a member of for three years. She knew NOBODY there. Several weeks later, we were walking in together and she HIGH-FIVED the guy at the desk, called him by name and asked him about his girlfriend's college exam..??! I had been signing in and out of the gym for three years and had never exchanged more than a polite "hello" with him. I didn't even know his name. Likewise she knew most of the ladies in our Zumba class by name and was making lunch plans with some...??!! I knew NO ONE IN THAT GYM!!!! So you know what I did? I started looking around, smiling, making small-talk in classes, learning names, chatting with instructors. And voila. I have lots of friends there now. But I had to change my natural behavior.
Sometimes shyness and a history of being introverted keeps us from being the fun and caring people we need to be to attract and keep friends. And some of us are just happier with less friends. But if you want more, go make them!! And it's a great example for your kids, who probably don't have your "problem" yet. But even if they are somewhat introverted, you can teach these lessons and show them a mom who has lots of people in the community who are friends.
Invite yourself into those weekly play dates if you want to go! Or the next time something like that happens if that was in the past. Unless these people don't like you guys, they're not going to refuse to let you attend! They somehow just figured you weren't interested, or they didn't think about you at all. Or you weren't as bubbly and engaged when the meetings started or whatever the magical spell is. but go, be fun, and have fun, and invite yourself several times if you must. And you know what? Since they all know each other better, you may be the odd man out for a few play dates. No worries! Just be cheery and don't try too hard. Say a cheerful goodbye after. Unless you're magic and magnetic like some, you're not the only one who has to do this.