That's easy – they're formulated to kill insects, not arachnids. Most household "bug sprays" will sooner or later kill any spider that's directly sprayed, but have little residual effect against spiders that come by later.

What kills a spider instantly?

Mix one part vinegar to two parts water in a spray bottle. Again, spray these on all possible entry points for spiders, including windows and doors. Spray this every week.

What spray instantly kills spiders?

Vinegar: Mix equal parts white vinegar and water in a spray bottle and spray it directly onto any spiders you see. Vinegar contains acetic acid which burns the spider upon contact.