SSH key question

[MR ZenWiz]

I have three machines set up on my home network with remote file copy
and ssh interactions.  I have my desktop "base" machine set up for
password-free remote access to the two laptops, but for some reason, I
can't get the same access from one of the laptops back to the base.

I generated the proper keys with ssh-genkey, then I used ssh-copy-id
to send the keys to the target machine.  As I said, done from the base
to both of the laptops, it works fine.  I even have remote access to
my partners laptop from the base using her id for the remote actions.

However, from my own laptop, I can't get password-free access, via ssh
or rsync, to my base desktop.  I either put up with the password
prompt, or ssh to the base from the laptop and run the file transfers
from the remote base login to/from the laptop because that way it does
not require passwords.

What am I missing?

Sequences:

base: ssh-genkey
base: ssh-copy-id <laptop>
base: complete remote login
base: ssh <laptop> - password-free login

This works.

laptop: ssh-genkey
laptop: ssh-copy-id <base>
laptop: complete remote login
laptop: ssh <base> - requires I enter the password

This does not work.

Thanks.

Mark