My brachys did this (and they still do it sometimes) when they don't want to eat anymore. If they are not hungry, then a cricket may be dangerous, so they run.
My avics didn't do that, but I think that's because they have a nest to protect, so when they were disturbed they would hit the web near the intruder with their pedipalps, maybe just lo let it know that web had owner.
My 1.5" B. auratum just did this recently when it was in pre-molt. Like davidmmx said, it may do this when it does not want to eat anymore and food could possibly be a threat for it (i.e. when a molt is nearby).