The Architecture can't do that
This my friends is the Kiss of Death in software development. Want a surefire way to suck the air out of the room in seconds? Utter this line at your next feature review meeting. I love watching the room - scanning from developers to product managers to dev managers to sales to anyone else in the room - they are all looking at each other waiting for someone to jump in and offer some kind of an olive branch to let them breathe again. In the worst case, Sales starts to blame PM who starts to blame the Dev Manager who, if they are having one of those horrible days and is completely ignorant of the software suite, might look to the developer for answers.
The problem here is that it's the not the architecture of the product that can't implement the new feature(s). Of course it can, its software, you have IDEs, you built it, you can change it. Maybe you built it against some crazy convuluted design pattern that only Sara and her sister have full working knowledge of and they just bailed on the company and you really don't have a grasp on how it works or maybe its that the feature is so new that what you currently have in your software suite is completely irrelevant to solving the problem at hand?
These are not the faults of software architecture.
I've seen the look a developer has when he mumbles this statement for the first time, I've BEEN that developer who mumbles that statement for the first time. It's not a deer in the headlights look, it's a look of resignment where the developer starts to calculate all the different possibilities of what is being asked in the feature and they are evaluating it against what the system has and then factoring in how much time they have (there is a calculation here somewhere) and then it hits them - I can't give you what you want, when you want it without creating some steaming pile of dung that will do this and only this and become the bane of our existence for now and ever more. And the architecture takes the rap because it cannot quickly absorb the new features as fast as we thought it could, Widget A does not plug gracefully into the framework, instead it kludges in and requires a little finesse. Is this all bad, no not entirely, if this was the complete focus of your application/framework then yes this would be a bad thing, but in this case it is not you (as the developer) are trying to build a feature for a product for your company.
In the end, the problem is the delivery model.
No matter the role you play in feature delivery of a software product, when you hear someone mumble this answer your first thought needs to be to stop what you are doing and get to the bottom of the real issue (DANGER WILL ROBINSON! DANGER WILL ROBINSON). What really is the problem? Did we cut corners on the last release and now we are paying for it? We can fix that. Have we pushed out critical bugs that need to get fixed before we think about this? Are the expectations too heavy in too tight a timeframe? These are all questions that have nothing to do with the architecture and everything to do the management of the software.
When you dig into the reasons behind "The Architecture can't do that", it rarely ends up being the actual architecture but rather something else altogether that you never would have thought to be the issue in the first place.