I wrenched for a cyclocross team and those bikes see pretty torrential conditions. How are you cleaning the cables? If you're just cleaning them as they are on the bike it probably won't do much good. You need to take the housing out of its stops.
How to do this:
Rear derailleur: Shift your bike into the largest/inner rear cog. Now WITHOUT turning the crank click the shifter as if you were shifting into the smallest/outer rear cog. This will create slack in the cable and you'll be able to easily pop the housing out of its stops.
Front derailleur: Shift into the big ring. Now WITHOUT turning the crank click the shifter as if shifting into the inner/smaller ring. Again, you create slack and be able to pop the housing from its stops.
Brakes: You need to release the brakes. On a side pull there is usually a quick release lever on the caliper itself. On cantilevers you need to unhook one end of the straddle cable. Again, this puts slack in the lines and you can pop the housing out.
Once you have the housing free of its stops you can slide it to one end of the cable and wipe down the cable then slide it back to the other end and wipe the remaining cable.
It only takes a minute or two to do this. Do it after every wet/muddy ride and cables should last all season.
The more extreme and effective solution is to run full length cable housing. Basically if you have non stop housing from brake/shift lever all the way to the derailleur/brake there won't be as many points for grit to enter. This is how all bikes used to be but in the 80s everyone went to split stops because it was cheaper for manufacturers and also because more housing means more housing compression and that means spongier brakes and less precise shifting. Modern housing is much better than the stuff from 30 years ago so that need is no longer as great. Thanks to the rise of hydraulic brakes there are now little adapters designed to plug into the split cable stops to hold hydraulic lines in place. These same adapters can be used to hold full length housing in place and I've seen guys use them for the rear brake and derailleur cables on cross bikes. Here's an example: http://problemsolversbike.com/products/housing_guides