First you need to upgrade the site to a package that suits its needs. You can do this by using the below steps
Step 1: Login to WHM. Go to Account functions and click Upgrade/Downgrade an account.
Step 2: Select the domain to which you want to make changes and click Modify.
Step 3: Select the package to which you like the domain to be upgraded and click Upgrade/Downgrade.
If the problem persists then follow the below steps:
Step 4: Go to Account functions and click Limit Bandwidth.
Step 5: Enter the new bandwidth limit. Give the site 10 MB of additional bandwidth. Click Change.
Once done, Refresh the site in your browser.