What's your fit?

Stability is an average, the average cap use per second. So, while it is stable in that at 7.8% the cap recharge per second meets the cap use per second, your modules use cap at the beginning of their cycle in chunks called the "activation cost". At 7.8% you're not leaving room for the activation cost of all modules that you ingeniously forgot to stagger to maintain cap above 0%.

How in the hell do you expect the game to know the manner you activate modules in?

iam too lazy to move this manually into eft but "10mn MWD II" is wheres you making a mistake...

...a fit which reports as capacitor stable at 7.8% (providing I don't use the MWD)

As Kivena stated, peak cap recharge is between 25% and 33% capacity (well, Kivena stated 25% but the graph I recall peaks between the two). Therefore, if the fitting screen shows you stable at anything less than 25% then it doesn't really mean indefinitely stable. And if you're running any module which will spike your cap use (Shield boosters and Armour reps are the most obvious culprits but even Invulns...etc may represent too great a spike in some fits) then you're probably not stable even then - you'll drain your cap down to peak recharge, fire off a cycle on the spiking module and suddenly you're below peak recharge...

The fitting screen's calculation is not ideal, but then the older 3rd party fitting tools used to "lie" in the same way. Although the results were never accurate, provided you were aware of the limitations you could still guage performance reasonably well.

oh hey, its another thread where someone tries to use in-game fitting window data and ends up being completely confused. We get these threads literally every day.

As always, the answer is to use a 3rd party program for this sort of thing. In-game calculations for cap stability, dps, tank, ehp, and about 10 other things are consistently incorrect or lack the basic functionality to tell you stuff like "with the mwd online but not on" or "with everything overloaded." This has been the status quo since forever.

This guy is even over a year old.

Buddy..
In this specific case (MWD fitting) The EVE client does report the stability correctly.

What you think you are doing and what you are actually doing are not explained well by the game. but that does not mean that you are getting false information.

also they (CCP) know about this.

...stuff...

So here is the big problem with the cap simulator in the fitting screen. It simulates all online modules as if they were active. So in order to simulate all modules EXCEPT the MWD you would have to either remove it or offline it. However when online the MWD gives you a 25% penalty to capacitor capacity so you you'd actually be running the simulation with considerable more cap than you have once it is online (even though it is not active).

But this does raise an interesting point which is, there is no way to simulate capacitor for all modules except MWD which I think is a quite common use case.