You need to:

1. Aggressively clear your browser cache
2. Check your .htaccess file and other configurations at the host level that might want to redirect to the wrong version

base domain .htaccess:

RedirectMatch permanent ^/$ https://www.a4at.com/blog/$

Blog folder .htaccess:

# Apache configuration for b2evolution's base folder
# Lines starting with # are comments.
# Updated 2013-07-16

# PHP / SECURITY:
<IfModule mod_php5.c>
	# On some overly "secured" systems, the following may need to be added in each folder:
	# AddHandler application/x-httpd-php5 .php

	# The following will try to configure PHP in the way b2evolution would like it to be:
	php_flag register_globals Off
	# You may want to turn the following to Off on production servers
	# Please do this only if you know what you're doing and will be able to retrieve potential errors from your error log
	php_flag display_errors Off
	# The following is the same as 'E_ALL & ~ E_STRICT' (except those constants may not be available here)
	php_value error_reporting 30719

	# You may also need some of the following:
	# Increase memory limit
	# php_value memory_limit 256M
</IfModule>

# DISABLE LISTING FILES ON SERVER:
# Don't show directory contents (not desirable, especially for media folders)
Options -Indexes
# Note: if you have access to the command line of your server, it would probably
# be even better to type this:  a2dismod autoindex
# (This disables the directory listing module completely)

# DEFAULT DOCUMENT TO DISPLAY:
# In case no specific file is requested, we want to fall back to index.php
# In case some subdirectories are accessed, we want to display index.html
<IfModule mod_dir.c>
	DirectoryIndex index.php index.html
</IfModule>

# CLEAN URLS:
# The following will ensure you can pass extra params after the filename on the URL
AcceptPathInfo	On

# CATCH EVERYTHING INTO B2EVO: (even if no php file appears in the URL)
# The following will allow you to have a blog running right off the site root,
# using index.php as a stub but not showing it in the URLs.
# This will add support for URLs like:  http://example.com/2006/08/29/post-title
<IfModule mod_rewrite.c>
	RewriteEngine On

	# This line may be needed or not.
	# enabling this would prevent running in a subdir like /blog/index.php
	# RewriteBase /
	
	# Redirect to REST API controller:
	RewriteRule ^api/v(\d+)/(.+)$ htsrv/rest.php?api_version=$1&api_request=$2 [QSA,L]

	# Redirect any .htm .html or no-extension-file that's not an existing file or directory to index.php:
	RewriteCond %{REQUEST_FILENAME} !-d
	RewriteCond %{REQUEST_FILENAME} !-f
	RewriteRule ^[^.]+(\.(html|htm))?$ index.php [L]
</IfModule>

it will load https pages (mixed content) fine until I set the base URL in basic_config then it gets that redirect error

Its not cache (cleared) so.. HELP ME

How many collections on your install?

Have you checked all settings on this page: http://b2evolution.net/man/back-office-reference/collections/collection-settings/urls-settings/ ?

including the special "all" collection, we have 7 created.
its set to Extra path on index.php - http://www.a4at.com/blog/index.php/blog-path-name/

Its been set like this basically since we installed b2evo many years ago.

@ppnsteve are still having troubles with this?

Yup,
I can't get it to migrate to https SSL at all.

Again:

Have you checked all settings on this page: http://b2evolution.net/man/back-office-reference/collections/collection-settings/urls-settings/ ?

You cannot migrate to https by checking only one setting.

Hi
As far as I know, yes I've checked them all... and if I set https in the config, it gets redirect errors.

So, again tell me, what am I missing here? whet specific settings should I be looking at?

your help page is pretty generic and has nothing about setting up SSL.

I also tried to switch to SSL for one out of 6 collections (therefore I did not change the basic_config.php) But all other settings are adopted. (The problem of permanent redirect, as @ppnsteve described, did not happen. )
But the SSL Connection does not work correct.
After some tests I found out, that this is caused by the bricks_Skin. brichs_skin comes along with two different 1.0 version. I obviously used the deficient 1.0 Version. By using the last updates v 1.0 Version SSL works correct.
But this version shows a another bug. Images set to cover show up twice on the startpage. I hope that the developers can fix this bug.