I'm a new kid on the block here, but this seems like a potentially significant problem. I like Shal's suggestion of just turning off their email. Then you send them a message (maybe from a different account/email address) letting them know they have not been kicked out, but have a problem they need to address. That message should also have some helpful hints on how to resolve it. Putting a banner on the top of the page when they get online that also informs them of the same would be helpful.
I think that has 3 advantages.
1) They can still interact with the group, and for some online may be enough. Plus they can not say they they were "kicked out" of the group, which it would look like to the uninformed.
2) As Shal suggested, 3 day is not enough. Our group is made up of people who travel and may be out of touch for weeks at a time. When away, they may not have access to email, but could have webaccess. So they would be informed and could deal with it when they have better access.
3) And for the the not so tech savvy, it would give them time to wait for their grandkids to visit to reslove the problem.