If you are not able to receive emails in Mozilla Thunderbird, you can do the following:
1. Make sure your Mozilla Thunderbird has been configured correctly.
2. Make sure you are not having problems connecting to the POP3 / IMAP server:
3. Make sure you have not exceeded your mail quota.
If you are using cPanel, you can log in there and go to Mail, Email accounts. Increase the quota twice to make sure this is not the problem;
4. Make sure your MX records are correct.
If you are a SiteGround customer, the easiest way to fix similar problems is by using Siteground's DNS servers: