Controller does not open in CodeIgniter - .htaccess

Question

I have three controllers in CodeIgniter application - i, login and test.
All controllers perfectly work with /APP/index.php/ path - I can open /APP/index.php/i, /APP/index.php/login and /APP/index.php/test.
Controllers i and login work without index.php as well - /APP/i and /APP/login (I have a modified .htaccess file).
Controller test does NOT work without index.php - I get 404 error when I open /APP/test.
i is the default controller, but login is not default and it works (I thought it could be the problem).
When I added the 4th controller it also didn't work without index.php.
It gets even more weird - sometimes I can open /APP/test/some_function (and sometimes I cannot) and after this I can even open /APP/test. But then I cannot open it again this way. index.php way works all the time. Test controller has a really simple code...
So my question is what can possibly go wrong here and how can I make my controllers accessible without index.php?
Thank you very much for your help.
Below is my .htaccess file, I think the problem can be there:
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /APP/
RewriteCond %{REQUEST_URI} ^system.*
RewriteRule ^(.*)$ index.php?/$1 [L]
RewriteCond %{REQUEST_URI} ^application.*
RewriteRule ^(.*)$ index.php?/$1 [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ index.php?/$1 [L]
</IfModule>
<IfModule !mod_rewrite.c>
ErrorDocument 404 /index.php
</IfModule>

Answer 1

I now understand where the problem was, thanks to #w0rldart suggestion.
Actually, when you access the controller without index.php file, the main application folder becomes case-sensitive (APP in my question).
As I have a much longer application folder name and it has both lower and upper case letters, I just had it typed with one letter in the wrong case. For the default controller it does not matter and other controllers were accessed via the links where the case was correct.
And as test was accessed directly, this wrong case was giving me 404 error.
Via index.php path the case of the main application folder doesn't matter.