I have Solus installed on two computers and with the last two updates eopkg dropped out about eight times on each. I presume the problem is with the mirror or the internet. To help me understand the issue I'd like to know if there's a day and time when the mirror is little used so I can update then and see if there is any difference.

I'm in the Pacific time zone which is UTC minus seven hours.

In case it's of interest the output of 'eopkg lr' is:
https://mirrors.rit.edu/solus/packages/shannon/eopkg-index.xml.xz

Thanks,
Mike

Unfortunately the mirror can be flaky. Sundays can be bad. Persistence is the only solution right now. The Core Team is aware of mirror issues. See, for instance, here.