Buy replacement dust covers.
http://www.bikeforums.net/showthread...t-cap-resource
or
Shove grease in after every rain
or
Duct Tape or other home made /adapted cover (as suggested by dabac)
or
Do nothing and ride till they break.
Good pedals are worth buying new caps for and rebuilding (replacing balls and regreasing) Its not hard and you will be glad you did.
IMO, Cheap pedals are worth rebuilding if they can be.
Pictures would get you More informed and focused responses.