The title says it all; I'm just having trouble finding a definitive answer. I suspect someone who breathes normally would lose the ability to hold their breath when stunned. Sure, they would breathe normally on reflex stunned on the ground, but wouldn't holding the breath be something they'd have to focus on?
If you aren't breathing, there's no reason why being stunned would force you to start breathing. You're only stunned, not unconscious.
However, this ultimately comes down to whether or not the DM considers holding your breath to be a free action (something which takes very little time), or not an action (something automatic that takes no time). This is because, according to the SRD page on actions, a stunned creature cannot take actions:
A stunned creature drops everything held, can’t take actions, takes a -2 penalty to AC, and loses his Dexterity bonus to AC (if any).
This raises the question: Is holding your breath an action? The description only says that you can hold your breath:
Any character can hold her breath for a number of rounds equal to twice her Constitution score.
This does not define it as a specific action, not even a free action. This supports the idea that it is not an action. It does not have to take place on the character's turn, as actions almost usually do, otherwise you would drown before you got to hold your breath.
A reflex save, similarly, is not an action; using your shield's AC bonus is not an action; these are things that you do reactively in response to danger, and you can do an unlimited number of these per turn. This suggests that holding your breath in response to falling into water is something you can automatically do.
It's also the case that the player typically doesn't have to declare their intention to continue holding their breath. It's not an action to continue concentrating on a spell, for example (although it is a free action to end concentration on a spell). You don't have to hold your breath over and over again on your turn, you just have to keep not breathing.
Consider also the rules on extraordinary abilities:
Using an extraordinary ability is usually not an action because most extraordinary abilities automatically happen in a reactive fashion.
It seems certain that breathing is not an action, since it occurs automatically. The argument could also be made, therefore, that not breathing is also not an action. The definition of not an action is as follows:
Some activities are so minor that they are not even considered free actions. They literally don’t take any time at all to do and are considered an inherent part of doing something else.
A free action, however, is defined as follows:
Free actions consume a very small amount of time and effort. You can perform one or more free actions while taking another action normally. However, there are reasonable limits on what you can really do for free.
I don't think it's realistic to say, "You already did too many free actions so you don't have time left to hold your breath this turn." Especially if, as the question suggests, the character is already underwater when they get stunned; there's no reason why they would immediately start breathing.
In short, while this is plausibly something sufficiently vaguely defined that a DM would have to rule on it, ambigious D&D 3.5 rules are officially interpreted by comparison to other similar rules, and those similar rules suggest that continuing to hold one's breath while conscious is not an action, and therefore you can continue to do it while stunned.
Consider also that if you do rule that holding your breath requires you take an action, which isn't explicitly supported by the rules, you turn stun attacks into instakills when underwater. That's considerably overpowered for an ability readily available to a low-level monk.