I don't know if these relate to this issue, but here are two scenarios that I have found result in very slow processing for EG users, don't really relate to SAS or EG, and are very easy to fall into for new users.
1. Moving large amounts of data between machines. This can be because EG submits code to a server that needs to access data on another server, or because EG runs the SAS session locally, and the local computer pulls data from a server. The SAS session is actually doing next to nothing, just ticking along waiting for the data communication.
To diagnose this, if you can use performance monitor look for very high network card volume. Another option is to move the data to the machine that the session will run on, and then run EG against it.
2. Running an EG descriptive task (e.g. Summary Statistics, Summary Tables, Table Analysis) with either a very large (tens of thousands to millions) number of combinations of classification variables, or using a variable with very high cardinality as a classification variable. SAS will actually run this very quickly, but if you're requesting results in one of the viewable formats, rendering the formatted document will take hours, and may never return. HTML is (I think) the worst.
To diagnose this, set the descriptive task to save the statistics to a dataset and turn off all of the viewable result formats. EG may run very quickly.