What three events cause Miss Stoner to fear for her life and prompt her urgent visit to Holmes?

The most important event was the death of Helen Stoner's twin sister two years earlier. It is still vividly imprinted on Helen's mind, especially because the mystery of Julia's death was never solved. When Sherlock Holmes enters the case in order to protect Helen, he inevitably solves the two-year-old "locked-room murder mystery" as well as saving Helen from the same fate as her sister's. 
Another event that causes Helen Stoner to fear for her life and to go to Sherlock Holmes for help is her being only recently moved into the room that was occupied by Julia at the time of her agonizing death. Helen doesn't like being there. She can't sleep well in the strange room which keeps reminding her of the night her sister died in her arms. It is because Helen suffers from insomnia in this room, and possibly because she has intuitive suspicions of her stepfather in the room next-door, that she is awake at around three o'clock in the morning when she hears the low whistle.
It is this third event, the whistle, that causes her greatest fear and prompts her to leave for London as soon as it is daylight in order to bring her problem to the great detective. As she tells him during their interview:

"Imagine, then, my thrill of terror when last night, as I lay awake, thinking over her terrible fate, I suddenly heard in the silence of the night the low whistle which had been the herald of her own death." 

Helen doesn't know it, but the "speckled band," the deadly snake, must have been in bed with her at the time she heard the whistle. It would have been slithering silently up the dummy bell-rope while she remained in bed wide awake and only waiting for daylight before she could leave for London.