Trigger skills/items cooldown and cooldown recovery speed?

I have 4.72 attack rate(full buffed) for my frenzy which is 211.8ms attack time.
And now I got 20% increased cooldown recovery speed with peot's pen, so it could be 208.3ms for each trigger.

I just test it, but skill(only put one skill) on my poet's pen still not trigger every 2-3 attacks.
If I wear cooldown recovery speed boots, trigger skill will always trigger every attacks.

I've try different level of my blood rage, 18/20(which makes me 4.79attack rate and 208.7ms attack time), 7/20(which is 4.67 attack rate and 214.1ms attack time). Those will not trigger my skill every 2-3 attacks when I just have 20% increased cooldown recovery.

Anyone has any ideas?

This is quite anecdotal, but:

I have a VD Poet's Pen build myself I created myself, I have however looked up into details regarding the internal cooldown on triggers etc.

I do not usually have this problem myself, I do not utilize cooldown recovery items and my attackspeed is 3.9. I do have this problem when I lag sometimes.

I came across a few threads/posts that said that when you get close to the "perfect" attackspeed, it sometimes skips a cycle.

There are different theories on why this happens, but I guess it has something to do with ping to the server, latency or something else. I am no expert on these things, but this is what I found and I'd like to share it with you.

TLDR;

Try to be about 5% below the "perfect" attackspeed

or

"Perfect" Interval ms - Ping ms = Interval you want (I don't really think this will actually work, though)

No idea this will work, but you can always try