some cats are ground hunters and some are air hunters. if your cat doesn't play with floor toys, mice will not be a 'target' for it.
maybe you could feed the mouse catnip!
do what my neighbor did....screamed bloody murder. mouse dropped dead of a heart attack!
mice are tricky, smart and fast. if there is one, there is probably more than one. use several traps.
most mice come in, no joke, right behind you when you enter the house. they wait by the stoop...