Well, i tried your system in my redstone world, and i managed to reproduce the problem.
In fact, some droppers randomly do not shoot. Most of the times the same three, but not always. I thought it was some kind of issue related to some block upload detection...
But not worry my friend, i managed to fixed it! Just a line of repeaters and it's done.Not so elegant, but it works fine. See this.
Now it shoots exactly 16 items each time the button is pressed :)
May i take your time for a longer answer?
First, i couldn't reproduce your problem, as stated before by @QbsidianH20
Second, after your first filling of the droppers, seeing your hoppers configuration, you will gradually start to make useless the top ones, then gradually the bottom ones too, starting from the far right (facing the front of the droppers), eventually ending with only the first one or two shooting. Tis is because of the way hoppers work, prioritizing vertical transfer over horizzontal.
This is true for each hopper system with only one input of items, like i see in your configuration.
Moreover, hoppers can only transfer items at a pace of 2.5 per second, making that huge set of droppers completely wasted, sadly.
If you have more items input from different hopper chains, i will suggest you to make a single dropper with clock for each input, maximizing your efficiency both of resources and time.
With your permission, i will proceed to illustrate.
First case: ONE INPUT
I copied your configuration. You can see after a while only the first dropper fires, but they are all powered! Fact is, he is the only one with something inside to fire. Poor guy.
Possible solution for one input:
Mono input, mono dropper. The clock on its back is a pretty nice one, only triggers when something's actually inside, staying off when empty. And still quite fast.
If you have a HUGE and i mean reeally huge amount of items to funnel, i suggest to simply copy this configuration as many times as needed.
You can see THREE INPUTS of items into three different droppers, each one with its own clock to minimize unnecessary ticks.
For each dropper we have five hopper lines, all converging into one input.
I have a humongous mob farm with a ridiculous amount of item drop per second, and this is my system. Three droppers don't even need to work all the time.
I hope i managed to help you, good luck building the rest of your farm! ;)
My farm and the funnels for sauce, with the firing mechanism (you can see it shooting items in the drop pool below, in order to be sorted).