I'm not sure that I have understood properly, but ...
Splitting a MIDI clip only sets that start and end positions within the clip. No notes are deleted. After the splits you might try Glueing each clip separately.
If that does not help, perhaps you could compress two
ataes states of a simple problem project file (no audio samples needed) into a ZIP file and post it here as an attachment so that we can have a look at it and see what's (not) happening? The two states are before you have split the MIDI track and afterwards, indicating what has gone wrong with a few screenshots.
How to post attachments (in Post #1)
How to post screenshots (in Post #2)