So I have time warner cable, and if I as much as touch the cable going to my computer or move the modem the internet disconnects for a minute then comes back on. Why is it so sensitive? The TV doesn't stop working and they both run off the same cable.
You either have a them loose at a connection point and are breaking the connection/causing bad noise [reflections or just opening]as it causes an impedance mismatch, or you have a broken fitting, generally it would be a common point so if you have a 2 way splitter, I would suspects the jumper going to the wall from it.
the third and less likley situation is you broke the center conductor inside a cable and the movement is separating the pieces and reconnecting them back and foirth.
Safest fix get a new cable from a Time Warner tech, and tighten it with a pair of pliers or 7/16 wrench lightly do not try to break the fitting as they do break rather easily, weight of your arm is enough to tighten it, no muscle needed.
Simplest fix [somewhat risky without a meter to see whats going on], tighten the old wires with a pair of pliers or 7/16 open ended wrench. Most people cannot finger tighten cables, unles they do it for a living. Got to build up that torque over years. You can use one hand and gently move/shake the cable while twisting with the other and usually get further as the threads unbind and rebind back and forth but the wrench and weight of your arm works much better, IMHO.