As Gail has said several times you aren't giving us much to go on.
First thing to try is spreading out the SSIS activity so fewer things are running concurrently. You have likely reached what I call the "exponential breakover point", whereby one or more resources is so exhausted that things slow down exponentially due to the overload.
Much more importantly is to bring on a qualified performance tuning expert. You could go back and forth on this issue for days or weeks and never get is solved via forum posts whereas a good consultant could isolate and resolve the issue(s) in a matter of hours or days.
Kevin G. Boles
SQL Server Consultant
SQL MVP 2007-2012
TheSQLGuru on googles mail service