In our case, we were using Hibernate and we had many variables referencing the same Hibernate mapped entity. We were creating and saving these references in a loop. Each reference opened a cursor and kept it open.
We discovered this by using a query to check the number of open cursors while running our code, stepping through with a debugger and selectively commenting things out.
As to why each new reference opened another cursor - the entity in question had collections of other entities mapped to it and I think this had something to do with it (perhaps not just this alone but in combination with how we had configured the fetch mode and cache settings). Hibernate itself has had bugs around failing to close open cursors, though it looks like these have been fixed in later versions.
Since we didn't really need to have so many duplicate references to the same entity anyway, the solution was to stop creating and holding onto all those redundant references. Once we did that the problem when away.