Bizarre MIDI behaviour..

I'm sure this is probably too simplistic, but have you checked the velocities?

what are you using for output?  some softsynths like GPO use non-MIDI standard CC's for volume and expression.  try inserting just TTS-1 for the output of that specific track and see what happens.

Could the volume changes be on another track?

1. With some download midi files there can be hidden data at the start of the track with the clip starting later Eg. data at 1.1.1 but clip starts at 2.3.1. 
    Solution here is to drag the clip edge(but not the clip itself) right to the start of the track view ie. 1.1.1

2. There may be a Sysx file associated with it. 
    Delete all lines in the Sysx file with data in them.

3. There may be 1 track that has all the controller values/ patch info for the entire project
    Delete that track.(make sure you have your original file saved before making changes indicated so that you don't lose any vital information by doing of the above if it does not solve the problem and introduces a new one)

4. As indicated in other responses the controller for volume(expression) may be different than individual track volume.  In other words 1 controller would control the individual tracks volume,  another controller would control the output of the Sound canvas as a whole.  If they are both defined as the same thing then the overall volume would jump to the value of whatever track is currently in focus.
     One solution for this would be use individual instances of the SC for each track to prevent overall volume from randomly fluctuating. 
    The best solution would be if you are able to have a different controller for each function. Eg CC 11 for each tracks volume and CC 7 for overall output volume of the SC.