You may have several issues here. First you live in the flat state of Illinois which can be very windy. A possible shingle choice for you are shingles rated for windy or coastal applications. They are made by the same manufacturers as those available to you for standard shingles. These shingles are made differently to better hold up to high winds and hurricanes. You would have to specify them with the experienced roofing contractor and special order the shingles for the replacement from the manufacturer.The high wind shingles have more adhesive between each shingle to create a sheet-like surface that holds better in the wind.
The second issue is the ridge vent and the cap shingles blowing off the ridge vent system. You can install the ridge vent shingles beginning in the other direction, say start at the south applying toward the north to change the direction of the exposed raised edge of the ridge cap shingles. This may keep the shingles on the roof longer if one direction of wind is more prevalent by keeping the raised edge down wind.
If wind is really a continual problem then change your attic venting from the ridge cap vent system to standard low profile pan vents. Remove the ridge cap system, shingle cap apply over the ridge of the roof and then install the pan vents. The pan vents are rated for higher winds.
Third is how the cap shingles are attached to the ridge vent system. Change the fasteners to those with plastic tabs on larger headed nails. Your manufactured home may have the roof applied with staples and not nails. The larger the heads on the fasteners – the better the ability to hold down the shingle in windy conditions. There are brightly colored plastic tabbed roof nails that provide much larger area “hold-down” ability for the shingles. These nails are fairly easy to find and are often used to nail down felt paper under the shingles prior to roof shingle installation.
Also, you may explore a threaded fastener with a much bigger head that the standard roofing nails for wider hold-down ability. Sometimes the ridge systems need a better fastener (screws and an adhesive) to stay attached to the ridge vent material. You can even put these plastic tabs onto the threaded screws if the roofing nails are pulling out of the ridge cap material.
Fourth is the roof type. Your replacement roof system must be installed with consideration for windy conditions. Every house location is different with topography, trees, terrain, nearby houses and wind direction all affecting the longevity of the roof. This means that your nearby neighbor’s house may not have this wind issue but you might. Your next roof choice must be one rated and installed for windy conditions whether it is a metal roof, composition or slate or tile material. Find a really good roofing contractor that understands these issues. Good experience, guidance and roofing material knowledge will guide you to a long lasting roof system that sheds the water, vents the attic and stays put. A metal roof can be installed to withstand the windy conditions or to blow off with a windy day. Material quality and longevity is either maintained and extended by experienced roofers or destroyed in the hands of poorly trained or inexperienced installers.