All Google Gmail accounts have a limited amount of bandwidth. Certain activities that transfer large amounts of data in a short period of time (like synchronizing a Gmail account to a mobile phone or mail client), can cause an account to reach the bandwidth limit.
Sadly, these limits will also apply to cloudHQ Multi Email Forward, Gmail label sharing, backup, or sync since we share bandwidth with other systems accessing the email (iPhone, Android, etc.).
The following limits apply for Google Apps for Work or Education editions. These limits may change without notice in order to protect Google’s infrastructure.
The limits for free Gmail accounts might be even stricter. Google does not publicly disclose them.
Gmail upload/download bandwidth limits:
See the Google support note on bandwidth limits for more details.