I don't think this requires storing anything on the server. That was kind of the point of the whole "store the server state in the continuation token"-thing :)
You want to store enough information in the token that you can easily reconstruct and resume the enumeration.
For example, let us say that the user asked for all comments with a score >= 5 sorted by post time. In that case you could return 100 comments, and a token that encoded something like:
{
"min_score": 5,
"sort": "post_time",
"resume_from_post_time": "2015-05-07T05:34:02Z",
}
To ensure that it is easy to resume the enumeration, the API can fudge the number of returned items so that the returned data always breaks at a nice "post_time" boundary. The goal here is to make it easy for the client to get all the data in the enumeration without implementing all this logic themselves.
True, it will only work efficiently for some types of queries, but a lot of the common queries can be reworked into something like that.