Do you know your people well enough to pray for the ordinary?

In church we pray for the big things.
In private we pray for the big things.

Because we know about the big things.

We're aware of the marriage which is on the brink of divorce.
We know about the family with a chronically ill member.
We hear when misfortune happens and people end up in hospital.

And we should pray for the big things. Earnestly and often.

But I wonder, should it be a marker of a churches pastoral care network that they are able to pray for the things going on in someone' life which is not "this-is-serious-enough-to-be-put-in-the-notices-and-emailed-around-the-prayer-circle."