1. You can try to get a static IP address from your internet provider.
2. If your ISP doesn't provide these, you can get one from any reputable VPN provider. You should make sure that the server you're connecting to is from the same country as yours, otherwise your Bittrex might get flagged/locked for "suspicious activity".
If you're not willing to pay (both of the solutions I suggested comes with a fee) then it might be better for you to switch to another exchange.
If it's not a VPN offering residential IP addresses, then VPN usage can also be easily detected. Even with the right VPN, I'm not sure there are any that allow the user to always use the same IP address. Even then:
https://medium.com/@ValdikSS/detecting-vpn-and-its-configuration-and-proxy-users-on-the-server-side-1bcc59742413(not sure what/if Bittrex is doing exactly to detect so-called 'suspicious' activity.)
It is possible that conflict between mail servers is the problem of delays? So the situation may improve when I change my email address?
Try gmail if you haven't tried already. If the problem persists, I doubt any other email provider is going to help the situation.