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The cause of this problem is very simple. The step through frame usually has a lower cable routing that goes underneath the brake caliper. This exposes an opening to the elements and water can seep in. May it be a casual ride in the rain or the bike being stored outdoors, the water will sit there and create rust that will weld the cable and housing in one single piece of rust. To prevent this, insert a few drops of oil down the housing at the same place the water gets in or cap it off with a dab of grease or do both. Do this once a season or more if the bike is exposed to rain on a regular basis.
Some of you have asked me why does a woman's bike have a lower top tube. It would seem more logical that this would be more practical for men! We have to go back in history to find out why. Back in the late 19th century when the safety bicycle (that's the name for the current rear chain driven wheel bike design) was invented, women rode their bikes with big skirts and dresses. This was not an option for the ladies of the time, it was the everyday dress code. It was very unladylike to throw a leg over the back wheel to mount and a dress over a top bar would have been just as bad. So bike designers of the time solved this problem by making the step through frame. To this day, for some odd reason, most bikes for women are still made that way. But a real woman's frame is one built to accommodate their shorter torso and longer legs compared to the men's frame. Ask your local bike shop about a real woman's bike. If they are any good, they should know what you're talking about.
Til next time ride safe and Godspeed.
Gerry