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):

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.

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:

• Casting another spell that requires concentration
• Taking Damage (and then failing a save)
• Being incapacitated or killed
• Actively choosing to end concentration

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.

The Sage advice response has the force of errata inasmuch as it changes the rules. Consequently, although no support is present for this in any book, making an opportunity attack will cause you to lose your readied action. However, since the Sage advice column says nothing about any other sort of reaction or reactions in general, you can still use those without being arbitrarily penalized, should you have any non-spell non-opportunity attack actions available to you.

I have reviewed the PHB, DMG, XGtE, and the Sage Advice Compendium for any rules relevant to the situation, and unfortunately, none of them explicitly bring any clarity here.

The best we can do is make a reasoned DM ruling from what we have, and the quoted Sage Advice question gives some guidance.

Since the Sage Advice ruling is specific to opportunity attacks, I would rule that we can understand from the ruling a sense of the intended general equity of the ruling, which is:

You stop readying an action if you take a reaction.

The SA ruling does not explicitly follow from any of the explicitly stated rules in the sourcebooks, so the best we can do is infer this ruling from the SA question and answer.

For this reason, I would rule that your concentration ends if you take any reaction while readying a spell.

Sage Advice does not require additional support.

To answer the last question first, as of the Sage Advice Compendium v2.3 (from mid-2019), they added this statement:

Official Rulings

Official rulings on how to interpret rules are made here in the Sage Advice Compendium by the game’s lead rules designer [...]

The Sage Advice answer is considered an official ruling and needs no support from the book; it acts as a clarification to the rules as written.

You lose the spell when you take a different reaction.

To me, there doesn't seem to be a need for a specific rationale beyond the SA answer -- if you use your reaction, you are no longer ready to react to the trigger because you went and did something different instead. You allowed yourself to be distracted from your readiness.

The rest then follows logically: Taking a reaction causes you to stop readying an action. The ability to concentrate to hold a spell is an aspect of readying, which you are no longer doing, which means you can no longer concentrate on your spell. Thus, you lose your defense bonus.