I use a Roland RD-2000 keyboard (Synthesizer)
Video clip of amplifier displaying the damper pedal: https://www.youtube.com/watch?v=An_1p62AyhQ&feature=youtu.be
Video clip of SeeMusic application not using it: https://www.youtube.com/watch?v=nEQAfruqo2Y&feature=youtu.be
Thank you for making the video showing the issue.
Have you tried recording the MIDI file in an app outside SeeMusic, like Garageband or Logic?
If the recording works fine in a 3rd party app, I would recommend doing the MIDI recording outside SeeMusic, then importing the MIDI file to SeeMusic after recording.