My mother has advanced MD and has had injections into one eye for this. The other eye was deemed too bad to treat by the time she was seen at the hospital.
She has no dementia diagnosis but (like all our ERs, I think), definitely has cognitive dysfunction. She managed the injections pretty well though.
Eventually there came a point where the treatment ended as the consultant felt that the situation was stabilised and there was nothing else to be done. I can't remember how long that took - about 18 months in total, I think.
I think my DMs eyesight has declined a bit further since then but of course other issues come into play, not least the cognitive problems. Also, injections are only suitable for wet MD and that can coexist with dry MD, for which there is no treatment. So yes, eyesight can (unfortunately) continue to worsen despite the treatment stabilising the situation that it's meant to treat. But I don't think the injections would be given for ever and a day; the treating team will assess each time and eventually they're likely to say that they've gone as far as they can.
My mum was very anxious around that point too, and I can't blame her; losing eyesight really does impact on a person's ability to care for themselves, and of course our ERs tend to be past the point of learning new tricks and new gadgets etc to help with limited vision.
One thing - is she still driving? You can still be legal to drive up to a point with MD but the combination of that and cognitive decline can be a killer (literally) behind the wheel, even if the person thinks they can drive.