Hi Sam,
I changed the properties of my package as you suggested. But, it didn't improve anything. I am adding an image which shows the various current sessions on the table and the it shows that the session of the SSIS package is being blocked by the session of the Insert.
The image might provide a better view of the Blocking problem.
SPID 66 is the Insert Query and SPID 71 is the SSIS task which is being blocked by SPID 66 and gets suspended.