Materials
Yes even in minor winds, those blue tarps are good for maybe 2 seasons. Sounds like your storage yard has some pretty extreme weather. Read about various cover materials at www.rochfordsupply.com. The newest materials are acrylics, and many combinations of acrylics and cotton (like Sunbrella). I have seen designs of boat covers that use bags that are filled with sand for weight and sewn to the edges of the tops cover. They can give a little but will add a lot of stability to a situation like yours.