I have been paged, but please never on grounds of "authority"; I feel more comfortable with "expertise", which probably prevents me from being full of crap, but perfectly allows me to be dead wrong.
Generally speaking ( I am not talking about James), and excluding (because already mentioned and / or hypotesised) ear-loss or gear difficulties, intonation issues at an advanced age are often a consequence of muscular decline and relative unsound technical reactions to the problem. I'll try to break it into categories and examples, but please be aware I'm horribly simplifying and zooming on physical zones, while in reality the whole system goes literally from toes to forehead and it's inevitably connected. We are ever so often thinking digitally, but homo sapiens is an analogic being and singing is definitely an analogic technique.
1) Going over the note's centre (sounding sharp):
A) at a young age it's often due to incorrect abdominal technique; instead of syphoning air by hooking frontal and lateral abs (the muscles impeding the diaphragm's ascent), the singer "pushes" the air with the muscles around the throat. Such activity doesn't allow for a controlled flux and clashes with the oral cavity's "forecast" position for the desired frequence, almost always exceeding it.
B) At an advanced age, such "push" may very well be a sort of compensation for a decline of the cricoid cartilage, setting the larynx lower. The singer more or less instinctively feels the need to "help" the air flux that now has to deal with an augmented resonance space (the"room" where sound is built, where the soft palate is the roof and the larynx is the floor). A not technique-savvy singer may "push" just because he just feels weakened by age or low energy.
2) Going under the note's centre (sounding flat): at a young age it's almost always a technical shortcoming*, while at an advanced age it's often due to a decline of the palatine muscles (the roof I was rambling about above). The singers doesn't raise the palatine veil and he instantly loses the high harmonics in his frequencies (while, and here's the trap, sounding perfectly fine inside his/her head). The cricoid issue may still apply: a lowered "floor" makes it difficult for the air flux to reach the "roof" without adjustements. My wife (middle-age) is currently dealing with this, and it's a bitch of a problem.
*Worth mentioning, because an experienced singer may have structural technical shortcomings. The singer (and his/her ear) is supposed to set up the resonance space while breathing the air in, and when they get said air out (singing) they only have to keep the set position in place and let the flux run the course in reverse. Sometimes singers just inhale and presume to set space and intonation position "on the way out". It's a steep gamble when you're young, a lost battle when you're old.
AGAIN, this is very general and very superficial.