Can I have Gmail alert me when it is incapable to fetch mail from my various other accounts?

Exists a means to get Gmail to alert me when it is incapable to fetch mail from my various other accounts?

I have Gmail examining numerous accounts (under Settings → Accounts & Import), yet from time to time it falls short to connect to an internet server (generally since that web server is down).

If I enter into Settings → Accounts & Import there is a red caution message that it fell short, yet I might not see this for hrs or days.

Exists any kind of means to get some sort of advising on the major web page of Gmail? Maybe a message box or an e-mail.