No one is ever served by just one communication method -- and never will be. Remember before the Internet, when you could divide up volunteers by who liked to talk on the phone versus who was face-to-face only?
With things like YahooGroups, users can decide how they want to receive information -- immediate emails, daily digest emails, weekly digest emails, web only, or RSS. I think that's always the way to go -- pick a tool that allows each person to choose how they want to receive information.
The problem is with those volunteers who are truly "non-Internet", who don't read email every day and don't have a cell phone. Or are there some that don't use the Internet at all (have no computer in the house)? How many volunteers are these? As you say, some of them are your most reliable volunteers and, therefore, you don't want to lose them. If it's a reasonably small number, I suggest talking to these people one-on-one, telling each your situation and asking them how they would like to receive time-sensitive information (I'm assuming by phone?). Would a reliable volunteer you have that does use the Net be willing to call these reliable but non-wired volunteers each time there's something time-dated they should know about? (provided the number of such volunteers is reasonable). Phone trees have been a tried and true method of activism for many years pre-Internet.
The other suggestions about creating a way for your non-Internet volunteers to be brought up to speed are also good. Could you host an onsite workshop for these volunteers to help them with basic Internet use?