If a result of a query exceeds the amount of 1000 entries, limitations of the base technology depending on entries and fields amount take effect. The more fields a layer has, the earlier an error will be returned.
In such a case, our recommendation is to search only for one search field, i.e. OBJECTID, and connect the other fields via a WebOffice join. This way the tables will be queried using a JDBC connection instead of using Arc Objects.