Post is not moving and the error "Error: 12035 - OCISessionBegin failed with ORA-27140" shows up (4286387)

The Post queue was backlogged and not moving:

sp_ctrl (servername:2100)> qstatus

Queues Statistics for servername
  Name:  queue_name(o.SID1-o.SID2) (MTPost queue)
    Number of messages:     249975 (Age       165 min; Size        877 mb)
    Backlog (messages):     249975 (Age       165 min)

Though the status was showing it as running:

sp_ctrl (servername:2100)> show

Process    Source                   Target       State                   PID
---------- ------------------------ ------------ -------------------- ------
Import     NAME                  NAME Running               23975
MTPost     o.SID1-queue_name   o.SID2      Running               23881

The "show post detail" showed that it was not moving at all:

sp_ctrl (servername:2100)> show post detail

Host   : servername
Source : o.SID1     Queue : queue_name

                           Operations
Target     Status              Posted Since              Total      Backlog
---------- --------------- ---------- ------------------ ---------- ----------
o.SID2    Running                  0 07-Jul-09 16:24:13          0          0

   Last operation posted:
        Redo log: 0          Log offset: 0        
        INTERNAL OPERATION

   Post state                        : Waiting
   Activation Id                     : 0
   Last operation transaction id     : 0
   Number of open transactions       : 0
   Number of active transactions     : 0
   Number of messages read released  : 6510

   Number of threads                 : 0

   Operations posted                 : 0
   Transactions posted               : 0

   Insert operations                 : 0
   Update operations                 : 0
   Delete operations                 : 0
   Other operations                  : 0

   Key cache hit count