^^^ There's your solution. The issue isn't unique to the LPEQ, but can occur with any linear-phase equalizer.
 
One of many reasons behind the time-honored best-practice of holding off on mastering until the tracking phase is complete. Ideally, when you enter the mastering phase you're working exclusively with audio. (The operative word is "ideally". I violate the rule often!)

Just for the sake of science I made a test loop of snare hits on 16th notes with Addictive Drum 2 and looped it about 16 bars.  I set the tempo to 300bpm (yes I wanted to push it).  And added the LP EQ to the audio out track and loaded the 7 band initial setup (but moved none of the controls just the flat default).  Without the LP EQ you can hear a very clear pattern.  Turn on LP EQ and then try various MIDI buffers.  At 250ms (the SONAR default) it missed numerous hits.  At 500ms it still misses a lot of hits, not as many but very noticeable.  At 1000ms it sounded the same.  At 2500ms it was also perfect.
 
I really think SONAR should change how it works so that the MIDI prepare buffers is internally set to twice the computed audio latency or what the user specifies, which ever is highest.  That way this problem goes away and no matter how much delay I stick in the audio chain no MIDI notes will get skipped.  Too bad it's clearly a feature too far.

Thanks everyone for your enlightening suggestions.
 
Raising MIDI buffer times is something I confess to have known little about. I had thought that doing so would make the MIDI tracks lag behind, as the buffer is measured in milliseconds. 1000 ms sounds like a lot. So I did some tests bouncing to track an Addictive Drums clip, and then playing it back alongside the un-rendered AD MIDI track.
I bounced with the MIDI buffer at 250. I played back and there was no phasing between the two tracks (flipping the phase on the audio track cancelled some of the audio, with some still passing through). Then I raised the MIDI buffer to 1000ms and played back. I couldn’t hear any difference. There was no phasing. So I will be keeping the MIDI buffer higher than the default, maybe at 500?
 
By the way, my original post was really to find out if the LP EQ was buggy or had issues because I was looking at buying a professional mastering EQ. Normally I wouldn’t master MIDI – that is, I wouldn’t do a final master with un-rendered MIDI tracks. I was just doing a demo with different plugins, and it was the first time I have tried the LP EQ. Maybe I will use the LP EQ after all instead of spending more money...

The easy answer is easy.  Just set the LP EQ precision (Expert mode) to non-linear while tracking.  Done!
 
LP mode uses a look ahead buffer that messes with any real-time work.  So save the actual LP algorithms for mastering only, and use non-linear mode for tracking and mixing.
 
The latest version of LP EQ has two categories of factory presets, Mastering and Mixing.  The Mixing presets have non-linear settings by default.
 
The MIDI buffer size is something that should be extended regardless.  The default appears to be too low.