.htaccess HTTPS redirect gives a redirect loop - .htaccess

Question

I've tried two different methods of redirecting HTTP traffic to HTTPS in the .htaccess file, but both of them give me a redirection loop. Here's what I've tried:
RewriteEngine On
RewriteCond %{HTTPS} off
RewriteRule ^(.*)$ https://%{HTTP_HOST}%{REQUEST_URI} [L,R=301]
And also this:
RewriteEngine On
RewriteCond %{SERVER_PORT} ^80$
RewriteRule ^(.*)$ https://%{SERVER_NAME}%{REQUEST_URI} [L,R]
I get the same error either way. What would be the proper way to redirect to HTTPS?
EDIT:
Looks like the problem is that it's a subdomain, and the files for the main domain are in a parent directory. As a result, the parent directory's .htaccess must be overriding this one. However, I can't figure out which rule is causing the problem. Here's the .htaccess of the parent:
# BEGIN WordPress
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteRule ^index\.php$ - [L]
RewriteRule ^other/(.*) /wp-includes/$1 [QSA,L]
RewriteRule ^file/(.*) /wp-content/uploads/$1 [QSA,L]
RewriteRule ^ext/(.*) /wp-content/plugins/$1 [QSA,L]
RewriteRule ^skin/main\.css //index.php?style_wrapper=1 [QSA,L]
RewriteRule ^skin/(.*) /wp-content/themes/sirens/$1 [QSA,L]
RewriteRule ^ajax /wp-admin/admin-ajax.php [QSA,L]
RewriteRule ^wp-content/themes/sirens/screenshot\.png|readme\.html|license\.txt|wp-content/debug\.log|wp-includes/$ /nothing_404_404 [QSA,L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>
# END WordPress
<Files 403.shtml>
order allow,deny
allow from all
</Files>
## EXPIRES CACHING ##
<IfModule mod_expires.c>
ExpiresActive On
ExpiresByType image/jpg "access 1 year"
ExpiresByType image/jpeg "access 1 year"
ExpiresByType image/gif "access 1 year"
ExpiresByType image/png "access 1 year"
ExpiresByType text/css "access 1 month"
ExpiresByType text/html "access 1 month"
ExpiresByType application/pdf "access 1 month"
ExpiresByType text/x-javascript "access 1 month"
ExpiresByType application/x-shockwave-flash "access 1 month"
ExpiresByType image/x-icon "access 1 year"
ExpiresDefault "access 1 month"
</IfModule>
## EXPIRES CACHING ##
<ifModule mod_gzip.c>
mod_gzip_on Yes
mod_gzip_dechunk Yes
mod_gzip_item_include file .(html?|txt|css|js|php|pl)$
mod_gzip_item_include handler ^cgi-script$
mod_gzip_item_include mime ^text/.*
mod_gzip_item_include mime ^application/x-javascript.*
mod_gzip_item_exclude mime ^image/.*
mod_gzip_item_exclude rspheader ^Content-Encoding:.*gzip.*
AddOutputFilterByType DEFLATE text/plain
AddOutputFilterByType DEFLATE text/html
AddOutputFilterByType DEFLATE text/xml
AddOutputFilterByType DEFLATE text/css
AddOutputFilterByType DEFLATE application/xml
AddOutputFilterByType DEFLATE application/xhtml+xml
AddOutputFilterByType DEFLATE application/rss+xml
AddOutputFilterByType DEFLATE application/javascript
AddOutputFilterByType DEFLATE application/x-javascript
</ifModule>
# Test Code Snippet#
IF User Agent "contains WordPress"
RewriteCond %{HTTP_USER_AGENT} WordPress
RewriteRule .* - [F]