The Suppression Deficit
What older brains lose is not the ability to focus but the ability to shut things out. Adam Gazzaley's laboratory found that older adults raise brain activity for information they have been told to attend to about as well as young adults do, and differ in pushing activity down for the information they have been told to ignore. The dissociation is well documented within that research programme. The broader reading, that ageing breaks inhibition generally, is less settled, and meta-analytic work has found age-related inhibition deficits are not consistent across tasks.
What it is
The work behind the claim is the face-and-scene task: hold one category in mind, ignore the other, and watch what the visual cortex does. Younger brains damp the irrelevant category below the level it reaches when a person is doing nothing at all, which is the observation behind the argument that ignoring is an active operation rather than the absence of attending. Older brains do not damp it in the same way.
Timing tells the same story more sharply. In young adults the neural signature of suppression appears within about a tenth of a second. In older adults there is no sign of it until at least half a second has passed, by which point the irrelevant material has already been processed. Poorer suppression tracked poorer working-memory performance, which is what lifts the result above a curiosity about brain waves.
The founding paper is Gazzaley with Jeffrey Cooney, Jesse Rissman and Mark D'Esposito, in Nature Neuroscience in 2005. The broader idea that ageing impairs the inhibition of irrelevant information predates it: Lynn Hasher and Rose Zacks set out the inhibitory deficit hypothesis in 1988, and this is a specific form of it.