A family member's house was completely rewired in 2011 and has
arc-fault
breakers for the bedrooms. One of those breakers will not hold in at
all, even with nothing plugged into any of the outlets.

Is substituting a replacement breaker the most appropriate first step,
or is there something else to try first?

The AFCI is probably just doing its job. Swapping a new AFCI is a
simple step, but you will probably still have the same problem. In
addition to offering arc fault protection, the AFCI also has 30ma
ground fault protection.

I had an AFCI problem this past summer in a basement wired by the the
homeowners. In addition to multiple code violations, they used barb
wire staples on the wiring instead of cable staples. One circuit I
could not clear. I disconnected all of the wiring from devices and
splices and pulled out as many staples as I could, but it still would
not clear. I started cutting the line back until it cleared about 6'
from the main electrical panel. I refed the circuit from that 6' mark
and prayed. The AFCI held and continue to stay on with everything
reconnected.

When an AFCI trips it blinks a number of times to indicate what caused
it to trip. Do you have the AFCI instructions to interpret the blinks?

I think that you need to open up the outlets, lights, and switches on
that particular circuit and check for loose connections as your first
step in troubleshooting this problem.

I haven't yet set eyes on the breaker in question: I've seen only a
cell-phone photograph of it. It's a CH breaker with a "Test" button but
no indicator light. Looking on line, I see some CH AFCI breakers that
appear to have an indicator light and some that do not.

I am hoping I can set up a time to go there tomorrow and see what I can
find out. I'll start by disconnecting the black from the breaker and see
whether it still refuses to hold in.

And I just noticed that in the photograph his breakers have "PWD" on the
handle whereas ours have "SWD". What's the significance of that?

Correction: he didn't send me the cell-phone picture, but I thought it
looked like "PWD" when he showed it to me. In fact it was "SWD" after I
cleaned off the dirt, the same as ours.

First surprise when I got there is that there is no Main Breaker: The
feed from the meter goes directly to the bus bars with no intervening
breaker -- so I had to do everything in a "hot" box.

The breaker tripped even with the black disconnected, so I replaced it
-- after checking, with everything unplugged, the resistance of the
circuit it had been feeding: 10MegOhms. All is now well, and the new
breaker has both a red "Tripped" flag and an LED indicator.

Next to the panel was a duplex GFCI outlet showing a red indicator
light, but although it would neither reset nor trip using the Test
button it was "live," so I replaced that as well.

Perce

Thanks for the update. I am surprised that the problem was the AFCI breaker. I will keep that in mind.