If you are tying two Panasonic PBX's together with a T-1 and from one of those Panasonic PBX's you have analog lines to a Toshiba PBX the T-1 has nothing to do with your dial failures as it's not even in the picture. Unless I'm still not following you and if that's the case I'll back out and let someone chime in who may understand it all.
Bottom line a T-1 PBX to PBX that is slipping is not going to be a LEC or any other carriers problem.
