What can cause the "Zero Sized Reply" error?

Question

Squid

There is a project developed on Laravel 4.2. During development, I hosted on my windows server and there were no problems.
It was time to transfer everything to production on a third-party hosting, and then the problems began. Periodically, the site crashes with a "Zero Sized Reply" error.
Full error text:
The following error was encountered while trying to retrieve the URL
Zero Sized Reply
Squid did not receive any data for this request.
I understand that this error is being thrown by the Squid proxy. Technical support says that this is due to an error in the script, but, nevertheless, I do not see any errors in the PHP logs or in the Laravel logs.
This error appears periodically, sometimes disappears after the first page reload, sometimes after the 15-20th.
Tell me where to dig?