Do you suppose there is a "natural max" of connections one is primed to keep in touch with? That after that number, it becomes more or less a task rather than reaching out out of genuine interest.

I think there are more parameters.

Some people's "natural max" for actively calling or messaging on a timescale of, say, weeks or months if there's no feeling of obligation is zero.

But it doesn't necessarily mean that aren't interested. Some of those people love keeping in touch when it happens - and are genuinely interested. Their "natural max" for people they enjoy being in touch with regularly (ie. not being a task) is much higher than the number they tend initiate things with.

Come to think of it that might be true for everyone.

Depends on how social you are and how much free time you have. Mentally, I think it can become taxing to reach out to that many people. So yeah, I suppose there is a natural max that depends on personality, free time, etc.