A bit of plaster advice please?

[cyberknight]

having kids that literally hang off the bannisters given chance i tried refilling and drilling the same spot and it just pulled out again , ended up with 2 at the top to stop it pulling out again

 

[T4tomo]

Make a bigger hole and screw a piece of wood (drill and rawl plug etc) into the brickwork behind the plaster just short of flush with the wall then fill around / over that piece of wood. Patch up the paint and then screw the bannister into the wood hiding just under the plaster.