How frequently you respool is down to a few factors, but Gardner's LEWIS READ offers us an insight into the science that should affect your decision...
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The simplest answer is that you should change your mainline as soon as you feel the performance has been compromised through wear and tear or the build-up of twist.
On open-water venues it may last a year, while on a weedy, mussel-infested big-fish pit you might find that it is mangled after a month of cajoling big fish through 101 obstacles!
Also, not all monos wear in the same way, and you will find that some copolymers, like HydroTuff, are better made to withstand abuse, while other lines, such as Hydro Flo, are made specifically for long-range casting and anglers that like a supple free-flowing mainline.
Copolymer mainlines don’t really dissolve, but they do get worn out and can eventually degrade from prolonged exposure to intense UV light.
That’s why it’s best to store lines in the dark, and once it’s on the spools I have never noticed an issue in the timeframe of the line’s working life. If stored correctly in a cool dark place it won’t deteriorate, potentially, for decades, rather than years.
It’s also worth remembering that 100% fluorocarbon mainlines, like Mirage, are not affected by UV. Fluoro also tends to last a lot longer on the reels because of its denser structure, making it very robust and more able to withstand general abuse.
I tend to change it (eventually) when it becomes scratched and battered (visibility issue) or simply too low on the spool.