It appears that a parent report refreshing also refreshes one of the child reports in my case its the first one in the list and for every refresh of the parent a new cursor is created for the child until you hit max open cursors.
Have a report that shows active sessions. If I set that to refresh every 5 seconds.
SID 4876 is my report refreshing.

Select from open cursors.
SYSDATE SID SQL_ID COUNT(*)
-------------------- ---------- ------------- ----------
Aug 01 2014 09:11:17 4876 0hm6ba4rbdbxp 272
Aug 01 2014 09:11:19 4876 0hm6ba4rbdbxp 273
Aug 01 2014 09:11:23 4876 0hm6ba4rbdbxp 274
The open cursor is for the query shown in the first child report tab which in this case is a select from v$session_longops.
Looks like this was reported back in 2007 as well Child Report Cursors Are Not Being Closed
I will try to reproduce this on the latest version of SQL Developer. The version of Oracle for this is 10.2.0.5. I will also try on version 11.2 which is the latest I have available.
Some Additional detals.
Happens on both latest SQL developer ( 4.0.2.15) and 11.2.0.3 of Oracle as well.
also can change the query in the child report to something as simple as select sysdate from dual and the same thing happens.
Message was edited by: Gamblesk