Oracle Stopping - Can't Login All Of A Sudden -
Start monitoring memory usage. Does your application terminate old sessions? If not, there is a connection leak that eventually takes away all processes your database instance can use and prevent new connections. There also could be a memory leak, that is why monitoring memory and swap could be smart to do.

Most likely to me seems to be the connection leaking. You can easily monitor this by making counts of v$session or v$process. These counts should not grow unlimited.
Since you use jdbc (thin client I asume) Dead Client Detection could also be useful. This gives the rdbms the ability to clean up unused sessions. Unused sessions are those that do not react upon a ping from the server.