Cause of 4.4.7 delivery failure

Here’s my error message:
Could not deliver the message in the time limit specified 4.4.7

The situation is domain A can’t is having trouble sending to us. They are the only domain that I’m aware of having difficulty sending to us. The user there says we are the only domain they are having trouble sending to (of course). My questions are what causes this? That’s all the info I have, so I don’t even know if that message go out of domain A’s network, right? I don’t have any server performance issues or Internet bandwidth issues. Any insight on this error or advice on handling it is appreciated.