Q:

Connectors that protect wires from breaking when it is resonating alot

I am building a robot vehicle, that is resonating alot when it is in rough areas.  Cause of this the wires in the robot will resonate a bit too.  When this happens every now and then a 'vein' (tiny copper wire in the wire) of the wire will break off.  After a certain time the wire will break off from the connector.  
Are there connectors that will prevent this?  Or is there another solution to prevent this?  I am currently using normal screw terminal blocks from TE connectivity.  The connector should be able to handle atleast 5A.

A:

You should stop everything flapping about.   In high vibration environments (aerospace, etc), you'd find everything tied or laced in some way to stop it shaking.   You might even find that the lacing has then had epoxy or some other sticky goop put on it to stiffen it further. 
Making everything stiffer will also raise the resonant frequency of the whole system, which may be helpful too. 
Here's a picture of the ultimate in robot vehicles for hostile environments (Curiosity) - note the lacing on the cables...

