Sure Google has a limit of downloads so that you don't abuse the system. These are the limits if you are using Gmail:
The following limits apply for Google Apps for Business or Education editions. Limits for domains during trial are lower. These limits may change without notice in order to protect Google’s infrastructure.
Bandwidth limits
Limit Per hour Per day
Download via web client 750 MB 1250 MB
Upload via web client 300 MB 500 MB
POP and IMAP bandwidth limits
Limit Per day
Download via IMAP 2500 MB
Download via POP 1250 MB
Upload via IMAP 500 MB