Something has possibly changed? Are you in control of your workplace's firewall? If not then check with your work's IT department to see if they've done something their end. I'm wondering if the remote connection is not being made because the local IP address handed out to your work computer is now different to what it was before, or they're using a segmented network and not facilitating VNC requests across the subnets.
". . . wonder if ARD can reliably do this kind of remote access work . . ."
ARD would not be my choice but it can work reliably as long as the remote location you're trying to connect to is set up correctly. If you're not the one doing that end of it then don't be surprised if you have problems.
". . . or if it is only reliable if both computers are on the same network intra-office?"
This is what ARD was designed to do and in my experience is the preferred way to use it. Having said that I've been using ARD for 18 years and it is not without its quirks and yes, its occasional unreliability. Apple have not fundamentally changed the way it works or addressed any of its oddness in all that time and seeing as they moved out of Enterprise capable software and hardware a long time ago I would be surprised if they address any of its issues any time soon.
My 2p.