SSIS Package Failed to Acquire Connection Intermittently

I have an SSIS package that first loads data from a source DB on another server to an intermediate DB on the same server as the SSIS package and then secondly loads data from the intermediate DB to a final DB (also on the same server as the SSIS package). I have 2 versions of this package, one where the initial DB is SQL 2005 and one where it is SQL 2008 R2. The destination server in all cases is SQL 2012.

Sometimes when I run the package overnight, I get an error that the SSIS package failed to acquire a connection, usually due to a login timeout error. My master package contains Execute SQL Tasks and Execute Package Tasks. The Package Tasks are all Data Flow Tasks. I'm using 3 project level connection managers, one for each database.

I have not seen the error when I run the packages during the day and it doesn't happen every night, just sometimes. In some cases, the master package will run several data flow tasks fine and then fail to acquire the connection on another data flow task, even though the connections are exactly the same. In the most recent failure, the connection to the intermediate database (on the local server) worked fine but when it executed the first task for the final database (still on the local server), it failed to acquire a connection.

1. Is there a way to handle such errors and have it retry the connections so it doesn't fail as often?
2. Is there a likely reason why the package is not able to acquire a connection?
3. Is there a way for me to determine why the connection isn't being acquired?

I've attached a screenshot of the error.

Thank you in advance.
Failed-to-Acquire-Connection.JPG