The War Wizard gets the Durable Magic feature at 10th level which states:
[…] While you maintain concentration on a spell, you have a +2 bonus to AC and all saving throws.
The Ready action states:
[…] When the trigger occurs, you can either take your reaction right after the trigger finishes or ignore the trigger. Remember that you can take only one reaction per round.
When you ready a spell, you cast it as normal but hold its energy, which you release with your reaction when the trigger occurs. To be readied, a spell must have a casting time of 1 action, and holding onto the spell's magic requires concentration. If your concentration is broken, the spell dissipates without taking effect. […]
Thus a War Wizard with a Readied spell would gain bonuses to their AC and saving throws. But what happens if the Wizard chooses to make an opportunity attack or use their reaction on something else? Do they maintain concentration on fire-bolt or do they drop concentration; Do they continue to benefit from Durable Magic or not?
The only thing I was able to find was that the Sage Advice Compendium document (pdf link) states the following (emphasis mine):
Q. I have a readied action. Can I stop readying to take an opportunity attack? Or is ready a full turn commitment?
A. If you have an action readied, you can make an opportunity attack, which causes you to stop readying.
Notably, this only addresses opportunity attacks and doesn't give any justification, so part of my question is this: Is there support for the conclusion made in the Sage Advice Compendium anywhere in the rulebooks themselves?
Best Answer
You don't lose concentration, but you can't cast the spell.
This really isn't any different than Readying the spell and either not getting the trigger you expected or opting not to use the trigger when it arrives.
But it is kind of a tricky situation, and while losing concentration makes sense at face value, there are rules to support that it doesn't - even if they don't really matter in the end.
Ready action
Let's begin with the rules around Readying (PHB, chapter 9) a spell (emphasis mine):
So we know that when you are readying a spell, you are concentrating on it. And you are waiting on the trigger so you can expend your reaction and release the spell.
Concentration
The four normal means of losing concentration(PHB, Chapter 11) are:
You have not crossed through any of these gates, so concentration is still up. There is nothing in the Ready action that says choosing not to release on a trigger (or the trigger failing to occur) equates to dropping concentration.
So what about the spell?!
Well, you are actively concentrating, but if you've expended your reaction, then you have no means of releasing the energy. Without the ability to trigger the release, the concentration remains until you lose your Ready at the start of your next turn (barring one of the effects that specifically removes concentration)
At that point, the spell energy dissipates without the triggering action and you can begin your turn as normal (minus any spell slot that may have been used for the Ready.)
Penalties
Given that the PC has already expended an action (and possibly a spell slot) and chosen not to use it by taking up their reaction, I really don't see a reason to further penalize them with the loss of their class feature as well - especially when it isn't fully supported in the written rules and only in a Sage Advice ruling.
But even with that SA Ruling, I don't see it as very well supported as I show above with this alternate ruling. They have taken their action to hold the spell, but have not released it. I see this as identical to ignoring the trigger and holding it until their next turn. The difference is simply that they used their reaction for something else, not that they dropped their concentration.