Well. It is an issue. Today i am lucky to have such a stable server, never one issue the last 5 years, or maybe once, but that's tolerable.
Try to communicate with your network provider perhaps?
I'm not sure i know what you're asking about offline, did you know there is single player in d2? ^^ Which requries no offline play, but also lack mulig options, severely limiting the gaming experience.
Back in the day when i had slightly more unreliable internet, i used to take it veeery slowly, killing monsters that appeared quickly and just taking my time. So that if something happened, i was relatively safe. Just never rush ahead and make sure you are overleveled+gear at all times so that you can survive for 10-20 seconds if lag should happen.