Things I don’t understand: magnetism

A stack of ferrite magnets

Image via Wikipedia

OK, I have a (astro)physics degree, so maybe I should understand this, but I don’t. Been meaning to ask my brother (PhD in high temperature super conductivity) – but never yet gotten around to it – so here goes.

For magnets to attract (or repel) one another, they must emit some sort of radiation: magnets cannot just “know” they are close by. So, what is this radiation? Presumably it is electromagnetic which presumes magnets are emiting radiation constantly.

Now, I am sure magnets (as in toy magnets of the sort pictured here) decline in strength over time, but they also seem to last many years with no easily noticeable sign of decline. So how can they emit electromagnetic radiation for years in this way?