There are two problems here, I suggest we concentrate on one, which is the File System out of resrouces.
As noted, this is mostly cuased by a bug in your download code where you are using up too many connections. Most likely I say, but not certain. But let us rule that out. .
Do you close the file connection and any other streams you use in a finally clause in this Thread? (you know, try/catch/finally)
You say you have closed the connections, but how do you know that you have? Are you logging something for each open and close?
As noted you are starting up a new Thread for this. How many of these Threads do you try to run at once?
