Does the age of the boiler decide it?
No. I've seen 20-year-old oil boilers around Cork still going strong, and boilers half that age giving nothing but trouble. When a boiler is giving trouble, I look at its age and what it's actually going to cost to put right.
When is a repair worth it?
I'd rather give someone a €250 repair bill than sell them a new boiler they don't need.
If it's a fairly straightforward repair, say a faulty pump or sensor, and the boiler is otherwise in good condition, I'd be inclined to fix it. There's no point telling someone to spend a few thousand euro when a repair could get them another few years out of it.
I also wouldn't recommend replacing a boiler until I'd checked that the problem wasn't elsewhere in the heating system.
When is it time to replace?
When it's an older boiler breaking down every winter, parts are getting harder to find, and the homeowner has already spent a small fortune keeping it going. That's a different conversation.
I wouldn't advise throwing €800 at a worn-out boiler if there's a good chance we'll be back fixing something else in six months.
What about running costs?
People forget efficiency. An older boiler might still be working, but that doesn't mean it's economical to run. With older oil boilers especially, it's worth comparing what you're spending on fuel with what a modern, properly sized system could save.

