There might be a grub screw some where, or it's threaded. It might be a two piece bolt like thing with a spring too. I think it should come appart. I haven't done a full disassebly of a long bobbin winder myself unfortunately. If you aren't completely sure the spring is broken and the trouble might cause by sticky grime you can try spray can oil. There probably are replacement springs for these. Some make their own by bending and winding a suitable wire into shape by hand, the tricky part is to track down the correct type of metal wire.
If you don't get anywhere contact Helen Howes, she has parts and knows the 28 very well. In the worst of case you can identify the correct winder (there are a few variants on the 28K),
Helen Howes has complete winders listed on her site (she has even more in storage) and there are usually some on ebay too. She might have the spring.