Hello,
On my rear wheel, the plastic spoke protector has started to rub against the spokes. This creates a very annoying noise while coasting. I have had this bike for about eight years and this problem never showed up until now. What could cause this to occur? My guess is that the cold and time is part of the cause.

Thanks.

Plastic spoke protectors will get brittle with age and exposure and eventually on of the prongs that clips over a spoke will break off and the disc will rattle annoyingly. Either replace it with a new one or discard it entirely if you trust your shifting adjustment.

You might want to make sure your spoke tension is still OK and that the nipple holes are not cracked or distorted. The spokes going slack might be the reason that they are now making noise, or, as Hillrider suggests, one of the little clips is broken. Otherwise I would just replace the protector. They are cheap and light and you will be glad you have it if you should for some reason shift your chain into the spokes.

While I'd personally choose option #2, there is an option #3.

Take a triangle Exacto blade and poke a few holes in your spoke protector. Then tie it back onto your spokes with some small zip ties.

The others have offered you good advice, but before you act on it you need to check how your protector is mounted.

Some protectors are wheel mounted and turn with the wheel, others are freehub mounted and turn with the cassette. From your description I suspect it's freehub mounted, especially if it's noisy only when coasting. In which case the one thing you cannot do is secure it to the spokes.

When buying the replacement you'll want one of the same type, or if changing from a freehub mounted to a wheel mounted unit, you might also need a small spacer to replace the protector's thickness on the freehub.

Thanks for the suggestions. I'll tried them when I get a chance.
To add further, the protector doesn't rattle instead it's pressed against the spokes. Looking at the spoke protector, there is no space between it and the spokes. I have looked at a another bike with a similar setup and on it there is space between the protector and spokes. This would confirm protector is mounted to the freehub.

Don't just guess by looking, it's easy enough to confirm where the disc is attached. Spin the wheel forward coasting, or back pedal and see which the disc turns with.