Splitting Clips Doesn't Work

Make sure the focus is on the clip not an envelope. Shift click on the clip header until it takes the focus. Alternatively change the selection on the track header drop down to clip.

I've had this happen if I'm using the Smart Tool+Alt and trying to apply split to either a mono clip that was converted to stereo, or vice-versa. Choosing the dedicated Split tool solves the problem.
 
There are some circumstances where the split tool doesn't work on a clip because it's not a "real" clip. For example, if it's being processed by V-Vocal as a Region FX you can't use the split tool.

Another possibility is that you have lanes open (perhaps with only one lane) and are trying to split the composite (track view) clip which won't work. Although unlikely if you've only just split it elsewhere, but if there's a bit of time between splits and that would be fairly easy to do.

Have you checked your snap settings? The only time I noticed this is when I had "snap to markers" engaged and set to snap to clip edges. I would try to split a clip and it appeared to not work, when in fact it kept "splitting" at the edge of the clip.

ston
Did the splitting of the clips create any orphaned notes (notes which extend either side of the split point)?
 
Sonar 'goes a bit mental' in this circumstance.  It just doesn't handle orphaned notes at all, i.e. I do not think any code has been written to explicitly manage this.  I say that because the software makes no attempt to ask any of the pertinent questions to the user which it should: "Do you want to truncate the note(s) to fit within the new clip, split the note(s) between the clips, or extend the clip(s) to incorporate the orphaned note(s)?"
 
I've seen Sonar exhibit really bizarre behaviour when creating orphaned notes by splitting clips.

OP's talking about audio clips, whereas it appears you're referring to MIDI. I don't want to hijack the thread, but I'll just say for the record that I'm not seeing a problem with splitting MIDI clips. What you get depends on the setting of Non-destructive MIDI Editing in preferences:
 
- With it off (my preference), SONAR will leave any notes that cross the split in the earlier clip, and the later clip will start with the first note after the split point. In this mode, the sound of the track is totally unaffected by the split. Initially it will look like the clips are overlapping in the same lane, but after toggling lanes, the later clip will be shown in a new lane.
 
- With non-destructive MIDI Editing enabled, the notes crossing the split get truncated by slip editing, and the later clip contains only notes that start after the split as before. The reason it's non-destructive is that either clip can be slip-edited back across the split to restore the full length of the truncated notes. But unless you move the split to a point where no notes are truncated, the track is going to sound different. I usually want to preserve the sound above all else, which is why I prefer the "Destructive" mode.
 
 

Have you tried turning off the Snap To/By feature? Sometimes if I'm zoomed in and try to split with it ON, I can't see the split because it split where the Snap told it to instead of where my cursor was.
 
Also, try Bouncing that particular clip, then try splitting again.
 
Steve

I have seen the same issue several times. Rebooting SONAR is the only way to get splitting work again.
SONAR X3 Producer x64 here.

Sounds to me like a maxed out buffer..... Somewhere!!

I have seen the case where I can't turn the split tool of when changing between projects using alt+w. I have to close and reopen to fix it. I wonder if the two are related.

 I have had this happen quite a few times. Restarting Sonar is my go-to workaround. At least I now know I am not alone:)

Me too. 
I thought I had executed some elaborate procedure to get in to this state, but it seems I'm not alone!
As far as I recall it's only happened since Cambridge (to me, anyway), I think
 
jdf

I have seen this issue as well. Only a restart of Sonar would fix it.

The same thing happened to me this morning.  I was going through the vocal clips I recorded yesterday.  I was splitting four or five clips at a time by lassoing them and using 'Alt+Click' on the selection.  The clips on the screen did not split.  When I looked at the Edit menu however, 'Undo Split Clip' was an option.  I closed Sonar and restarted.  After that splitting clips worked as usual.
 
Note:  After repeating this on three vocal tracks and using Melodyne for some pitch corrections, nearly all of the clips on one of those three vocal tracks had fades on them.  I haven't seen that happen before, but the the Smart Tool gave me the Crossfade Icon a few times, so maybe it was operator error.  I don't know.

Thanks Bristol, that seems to have cured the problem :