wp-login.php page loading very slow, all other pages fine

I have a wordpress install that updated from 3.8.1 to 4.5.3 a few weeks back. While I’m not sure this had anything to do with the update, the wp-login.php page on the site has been loading VERY slow the past few weeks. All other pages on the site load normally. This includes public pages, admin pages, and pages that I have restricted to certain users via the Groups plugin. All load fine. The wp-login.php page also loads normally when a user is already logged in. But if not already logged in, the page can take anywhere from 15-20 seconds to load.

Things I’ve tried so far:

1) Disabling plugins one-by-one. It does not appear to be a plugin causing the issue.

2) Contacting web host. I don’t know how thoroughly they looked into my inquiry, however their suggestion was for me to update from PHP 5.3.X to 5.4. I’ll admit I have not tried this yet, however it could be a headache and I’d like to try this last.

3) I created a copy of wp-login.php and the pages loads normally! This seems very strange to me? I then wondered if the wp-login.php page was being attacked. I have a history of logins in the WP dashboard and it hasn’t indicated any unusual logins or IP activity lately. So I logged into cPanel and went to Latest Visitor Stats and typed in wp-login.php. There doesn’t appear to be that much traffic from different IPs, however I did notice one IP that I do not recognize is getting a 403 status code about every 15 minutes. Not sure what this means, but thought it may be relevant?

4) Checked the memory limit of PHP and it seems fine, currently set at 256MB and using maybe ~75MB on average.

5) When inspecting the login page in Chrome, it appears the time for loading, scripting, rendering, and painting all seem normal. The idle time however is ~20 seconds.

6) Any other ideas/suggestions?

WP info:

WP Version 4.5.3
WP_DEBUG false
WP_DEBUG_DISPLAY true
WP_DEBUG_LOG false
SCRIPT_DEBUG false
WP_CACHE false

PHP info:

version 5.3.XX
max_execution_time 30
memory_limit 256M
upload_max_filesize 64M
post_max_size 64M

DB info:

mysql 5.5.48
key_buffer_size ~8 MB
max_allowed_packet ~16 MB
max_connections 450
query_cache_limit ~1 MB
query_cache_size 0
query_cache_type OFF

Any help would be greatly appreciated.