The quick answer is when they don’t sound as good as you want anymore.
Generally I’d say at least once a month if you play a few times a week, more often if you play almost every day. I know some professional musicians who change strings a few times a night, between each “set”.
Strings go dead for a number of reasons.
One factor is just “metal fatigue” or the decreasing elasticity of the metal as it is stretched and bent when you play. Some alloys are more resistant to this than others and can sound “bright” longer. I think phosphor bronze would probably be in this category, as opposed to softer alloys.
Another factor is the loosening of the grip of the outer windings on the inner core wire. Core wires are most often hexagonal rather than round in cross section to allow the outer windings to “bite” in a little better but eventually the windings lose their grip the strings start sounding dull.
Dirt or dried sweat gets built up in between the windings. This makes the strings less responsive and springy.
Finally there is the chemical reaction between your body acids and the metal. Some of us have more corrosive body chemistry than others. When I worked in Research and Development at Gibson we had one co-worker who could make strings turn black in a matter of minutes. We often asked him to test new string sets- if they survived his touch we knew they were probably going to be OK for just about everybody.
Some strings are coated with proprietary polymers to extend their effective life. These coated strings are often considerably more expensive than standard uncoated strings, but the trade off is they can last much longer. This technology has come a long way from when it was first introduced. Initially the coatings would sometimes fray and hang off the strings like strands of fine hair in the area where the pick would strike. Also the early coatings tended to be heavier and they dulled the sound of the strings, so they might last longer but never really sounded as good when new as uncoated strings. Coating technology has improved a lot but even now I must admit that for pure tone I still prefer an uncoated 80-20 bronze string. However they go dead much faster and you need to be willing to change strings much more often.
One thing you can do to extend the life of your strings, coated or uncoated, is to keep them clean. Take a moment to wash your hands before picking up your guitar, and wipe it down with a polish cloth a little before you put it away.
But sometimes you just need new strings ; - )
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