Setup Folder Permissions to Write "ini" File
 

Giving write permissions to all IIS_USRS group is a bad idea from the security point of view. You dont need to do that and you can go with giving permissions only to system user running the application pool.

If you are using II7 (and I guess you do) do the following.

1.    Open IIS7

2.    Select Website for which you need to modify permissions

3.    Go to Basic Settings and see which application pool you're using.

4.    Go to Application pools and find application pool from #3

5.    Find system account used for running this application pool (Identity column)

6.    Navigate to your storage folder in IIS, select it and click on Edit Permissions (under Actions sub menu on the right)

7.    Open security tab and add needed permissions only for user you identified in #3

Note #1: if you see ApplicationPoolIdentity in #3 you need to reference this system user like this IIS AppPool{application_pool_name} . For example IIS AppPool"DefaultAppPool

Note #2: when adding this user make sure to set correct locations in the Select Users or Groups dialog. This needs to be set to local machine because this is local account.
 
These instructions resolve this issue when trying to download the new ini file:
 

Error

An error occured while trying to process your request

Error details

Controller name:

SetupAdmin

Action name:

SetupIni

Exception detail:

Access to the path {root path for webManEx}"ManEx"App_Data"Setup"ManExSql.ini' is denied.

 
It will also resolve a similar issue when trying to upload files for import.
 

In case there are updates to the answer, here is the link to the original answer:

 

In some cases, users may not be able to load the app pool name as indicated.  If that is the case, they should add write permissions to the IIS_IUSRS to the APP_DATA folder.