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503 errors on cPanel accounts are almost always due to hitting the physical memory (RAM) limit for the account. Your site is still maxing out the RAM for the account. One thing you might want to try since you're using WordPress is a caching plugin. Good results are seen with the Cache Enabler plugin specifically. If configured correctly, a caching plugin should limit the resources needed for visitors to access your site.
If this does not resolve the issue, you may need to upgrade to a larger plan. Please contact our customer support for a more thorough review from within the account.
I can't even get to my wp-admin to download a plugin. Even when I kill all my processes the RAM slowly works its way back up to maxed but I still can't get in.
If you're not able to reach the admin area from inside the account, you can access through SSH, Please see the article here to setup and then use this option.