It could be that the surrounds are deteriorating, or it could be that something on the woofer is loose. Either way, it's fairly easy to fix and you shouldn't replace the woofers (first because repair is usually cheaper, and second because it's unlikely that you'd be able to find exact replacements, and any other woofer wouldn't work properly). First thing I'd do is carefully inspect the surround and the dust cap (that piece of paper or plastic that covers the center of the cone). Make sure the foam isn't disintegrating and that it's completely glued down. Check that the dust cap also is completely glued down. Even a very tiny gap can cause exactly the situation you're describing.
If that doesn't yield anything, the next thing to do is to carefully remove the woofer from the cabinet. Before you disconnect the wires in the back of the woofer, make a note of which wire is connected to which tab on the woofer. Then carefully inspect the inside of the cone. Look at the tinsel leads (the wire that go from the connection tabs to the voice coil) and make sure they only touch the cone where they enter it. Carefully push the cone all the way down and see if the leads make contact. If they do, that's probably the issue. If not, inspect the spider (that usually yellow or brown piece of stiff fabric with accordion folds, that's connected to the bottom of the cone and the frame). Check that it's completely glued to both the cone and the frame all around. Report back here what you find and we can take it from there.
