It doesn't sound like a memory issue, but if you are sure it is you could reduce the memory SQL Server uses just before the SSIS packages run and increase it again afterwards. There is no need to restart SQL Server to do this.
This SQL script will change the memory usage of SQL Server.
EXEC sys.sp_configure N'show advanced options', N'1' RECONFIGURE WITH OVERRIDE
EXEC sys.sp_configure N'max server memory (MB)', N'4000' RECONFIGURE WITH OVERRIDE
EXEC sys.sp_configure N'show advanced options', N'0' RECONFIGURE WITH OVERRIDE