Background
If you wish to keep a copy of your email in your personal Gmail account, do not use forwarding. Your account will get blocked by Gmail rate-limit eseocially when you use personal gmail account.
Solutions
Instead of using forwarding (push email toward gmail), you should use pop3 (gmail collect email from your inbox) feature that available in gmail.
Step
- Login to your gmail account
- click on gear icon and "see all settings"

- Go to
Accounts and Import>Check mail from others accounts>add a mail account
- Enter your company email

- Select
POP3and Next
- Enter your email credential and server name. You can select checkbox according to your needs and click add account

- Your email should show in your gmail in short while