www programming

ok checking this from scratch that i've no test after ...

it work here, so i suspect that the problem can be the plugin you use for users (which you have mention one time and i do not remember now)
i will follow test some more ...
i've create a subsite, and i can access it without problems with same user admin, even if plugin has not been activated into this created subsite.
But your repeating loop on redirect, let me think to something else about cookies (or about other plugin).

Sure you have setup cookies in the right way and phpBB cookies are recognized over all domain?
cookie setting:
.mydomain.com
logout, clean cookies on browser.
Is your example test online (i imagine no)?
I'll setup one as i can online for testing purpose.
In the main site all work fine? with wp_w3all active?
Let know ...

Cookies are set up as instructed.
The forum is live and active (since 2005) but the Wordpress side is not linked to it at present. It is online for testing only (link sent by PM).

I can visit network admin and the domain name subsite, but all other subsites get the redirect error.

I'm sure it may well be a conflict with the aMember software I'm using. There is a Wordpress plugin and a phpBB plugin within aMember. I have completely removed the Wordpress side.

It is difficult to remove the phpBB side at present because the forum is live and aMember provides the registration to this and a subscription area of the site. If I can get WP_w3all to play ball, I will remove aMember completely and use a Wordpress membership plugin for the subscription area.