The line droping is because the CiX is seeing the static as a CPC signal, if they do not have voice mail, you can turn that off. this will cause the line to stay up even with heavy static. If they have voice mail, you need to leave it on.

Sataic can come from lots of places, is it wet. Could be bad pairs from the telco, only has static when it rains. Bad connections at the system or interface. Gets static when the wires are moved. Did Suddenlink bring copper lines? or is this a T1 with a channel bank? Could be the T1 is slipping. Lots of things, just keep looking, you will find it.