MacOS – Macbook Air failing to reconnect to network after sleep

If the login functions through a Webpage, it's probable that the closest you could come is to write a script to fill in the form for you.

If you're lucky, the login form might use a HTML GET request so you could to bookmark the page that logs you in. Pay attention to what redirects occur once you login. If you see something like this:
http://example.com?name=fred&pword=qwerty, you can bookmark that and go to it to log in automatically.
This is unlikely, though, because it isn't a very secure choice for your company. The form probably uses a POST request.

I've had this exact same experience, though not every time. Sometimes it means sites that I have visited recently are unavailable but other sites I haven't visited in ages load just fine.

Usually flushing the DNS cache resolves it.

sudo killall -HUP mDNSResponder