My otherwise healthy Mother (93) has started breathing through her mouth. Is she losing the capacity to breath?

First thought would be sinus or nasal congestion. Also, does she eat high sugar foods? Are the room she's in dry and in need of humidity? Either of those could cause nasal congestion - they certainly do for me.

Check the side effects of the anti-vertigo meds; there might be some "critical mass" level as which use of them can cause nasal dryness or congestion.

My concern about mouth breathing would be that the amount of air intake isn't as great as it would be through nasal breathing. If you know how to breathe as a singer does, try that through the mouth and you'll find it's pretty limiting.

There's nothing particularly wrong about mouth breathing. Why does it concern you so? Could be a cold...sinusitis...habit...stuffy nose. It would have a tendency to make her mouth very dry, but beyond that, I doubt I'd pay any attention to that at all.

Does she appear to be uncomfortable or in pain?

Do you know what her wishes are for her medical care at this time? You say she is mentally sharp. Does she want to see her doctor?

It could be a sinus infection, cold, etc. You might discuss it with her doctor if you have Healthcare POA.