Midi Clip Audio Won't Stop Playing

Weird but simple problem: I have my synthesizer hooked up as a midi controller, and for ex. I use cakewalk sound center, and I picked a synth (this applies to multiple of them) and I recorded what would be used as a loop. Problem is, when I paste the midi file and play it back, at the end of the clip, the final note just keeps getting held out for as long as I have the project playing. It's not making much sense as to why, because I recorded it ending when the loop ends- and the piano roll shows the duration of the notes to be how they should. How come the audio just keeps playing though? It holds the last note (or chord, in my case) that I played and it stays the same and will go on for minutes if I don't stop the entire song. 
 
Note: when I copy and paste the clip in the proper size and place one next to it, the note being held out interlaps with the consecutive clip. Pasting one after it isn't stopping it either. 
 
Also note: I noticed that this problem seems to only be happening to sounds that naturally won't die off over time if you held the key down. I didn't realize that the piano from the sound center doesn't have this problem because the sound of the piano only lasts a few seconds if held down with keys. Synths, leads, etc, are the problem, because they will never die off if you held the keys down. Thought this might be important to what is going on.

What cut are you talking about? Just a little confused on what you mean to do. It's on a 4/4 time signature and it's a 16 beat loop. The clip normally gets cut right where the next clip is supposed to start, like a loop. What do you mean by a note on and a note off? 

It takes 2 midi events for a note.  The first event is a Note On event, which will contain data on which note is to play, etc.  There is a 2nd midi event required in order for that note to stop playing, and that is a midi Note Off event, which will contain data for which note is to be turned off.
 
While on the one hand, it takes 2 events for hearing a note play and then stop, it doesn't require data in between, so if someone was to hold a note for several measures, it would still only require those 2 midi events, even with all of that time the note is held.
 
Bob Bone
 

Hmmm... So, I use a pedal connected into my keyboard to help hold out notes, it makes it easier and smoother to play, of course. I would have used the pedal on these clips (I'm not home, can't pull up the file atm) so you are suggesting it may be because I didn't let go of the pedal in the recording, so the file doesn't know I let go of it? Which, would hold the note out forever if I kept the pedal down

Ahh yea, that would make perfect sense then. Wont be home till close to midnight tonight but when I do get home I'll re-do the clips making sure the pedal is released completely in the recording. Should work then. Thank you guys for the help!