This is a very common faxing problem. Sometimes lines are extremely busy which will typically give you a busy signal from the fax machine. However, it can just ring and never pick up if a call waiting is active on the other line. There could also be an issue with the fax machine that you are faxing to or the line on the other end may not be plugged in correctly to their fax machine.
These are all very common problems that we troubleshoot in our own environment.
What to do
If you are having this problem, please try and call the number directly from a regular phone. See if you can call through and verify that you hear the fax line pick up. This will tell you whether things appear correct on the other side. If you are able to get through to the fax machine, then try sending your fax again.