i fish a drop shot 90% of the time i spend fishing. i use 15lb braid to a 6lb fluoro leader, or 6lb fluoro. depending on what rod im fishing.
i use 6lb Seaugar red label, have not had line break yet. i use a palamor knot, and then stick the tag end back through the eye of the hook. when you are tieing your knot, its up against the hook right? not up high then sliding it down as its tight? ive seen some people do it that way and that just destroys your line.
with a dropshot, you dont need to set the hook hard at all, the hooks are so small, the penetrate the basses mouth very easily. i use either the vmc spinshot hooks, or the vmc sureset dropshot hooks.
what brand line are you using? the red label i use is pretty tough stuff, the part between the weight and hook is so abraized its not even funny lol i never change it though cause it just dont break. ive had the same hook on now for the past 5 fishing trips with out re-tying. i just feel the line from the hook up and if it feels smooth, i cast it back out.