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I am unable to reproduce your issue.
I am using FV 3.1 for now and have tested this using the built in SearchWidget and the eSearchWidget 3.1.13. Both are searching my event themes repeatedly and working fine
I even tried publishing on version 10 as well as 10.1 and, everything is working fine. (You need to register your datasource in 10.1 to publish an event theme to a service).
R_
Have tested using both an Oracle table and a FGDB table, both work for me.
Julie,
I think you will have problems until you get rid of the OID error as the layer is not searchable without an OID. See this post that is referring to the same issue (but for Oracle table) to see if it get's you on the right track.
http://forums.arcgis.com/threads/80419-eSearch-on-XYevent-return-only-1-result.?p=284530#post284530
Basically, I have an autogenerated, unique, non-null numeric field being added to my table. This way, Arc can use it as an OID so that it will behave as a normal layer (except for the real time updates of course).
R_