Thanks for the suggestions.

I tried switching to "Activity", but then again only the few posts of 3 months and such appear. I have tried both with and without the assets you recommended, the result is the same.

Then I tried creating a new menu item, with "Activity" (both with and without the assets) as well as with "My Activity", but there still the same results.

Then, I have tried something else: I tried with a test account which is only connected with two other users (my main account, and one other person). When I look at the activity wall there, I see the posts of my main account, as well as the posts of the second person. The posts of that second person, however, do NOT show up when I look at the activity wall with my main account (with the "My Activity" setting). So it would seem that my second test account shows more of its connections than my main (admin) account. So I'm wondering if this is a clue as to where to look for the cause of the issue?

Nearly all connections on my main account were established through the CB Auto Welcome plugin. Are they somehow handled differently than manual connection requests? Just in case we're on to something here, these are the settings for the CB Auto Welcome plugin:

Auto Welcome message: yes
Notification method: PMS only
PMS welcome subject: (some text filled out)
PMS welcome body: (some text filled out)
PMS sender id: 6838 (this is actually the user id of the second person whose posts only appear on my test account, although the connection there was also established automatically through the plugin)
EMAIL Welcome Subject: (some text filled out)
EMAIL Welcome Body: (some text filled out)
EMAIL Sender Id: 62 (62 is an additional admin account of mine)
Automatic connection to user: yes
Direction of connection request: key user request
Connection request message: (some text filled out here)
Key user Ids: 6838,64 (64 is my main account)

I have also just now tested between the test account and the additional admin account (with user id 62). I posted something with one account as "public". It did not appear to the second. When the second account requested a connection to the first one, the post did appear (even before the first account accepted the connection request).
Then I posted something with the privacy setting "connections only". Neither post appeared to each other as long as there was no connection request & acceptance. Once connection was established both ways, both could see each other's test post. The connection here was, of course, not established through the CB Auto Welcome plugin.

I'm aware that users have to accept the connection request first, and most of them do (I don't intend to force them to accept it). I get an email and PMS notification every time a user does. I have checked for several users that I am listed in their list of connections, and I only have the option to "cancel connection" (not cancel request). Yet, the posts of these accounts don't show for me when "My Connections" is set. At least not for my main account, as the test I did with the test account and second admin account did seem to work fine.

I just removed the connection with my test account (which had been connected with CB Auto Welcome), sent a new request which I then accepted with the test account. On my main account, I still don't see any post of the test account. The other way around, the posts of my main account disappeared on my test account's activity wall when connection removed, and showed up again when a new connection was established. So CB Auto Welcome is probably not the cause after all.

And yes, the thought just occurred to me as well that maybe it has something to do with the large amount of connections. I have nearly 2500 connections, mainly because most people accept the automatic connection request.

No php/sql error appears on the screen though. When I switch error reporting on, none of the errors/notices that appear seem to be related to this issue: