A fictional detective shouldn't be lovable, or cute or (God help us) sexy.
A fictional detective stands for Justice. And justice is cold and harsh and no respecter of persons.
Which is why Sherlock Holmes is the business.
You want warmly human? You want touchy-feely? Then give your detective a Watson. A Watson can be as cuddly as a cuddly thing with fluff all over it.
But your detective must be cold, hard, inhuman. (An odd glint of buried fires- a tenderness for some unattainable, long lost love- an Irene Adler- is permissible- but let it be only a glint.)
And let him/her be weird. The weirder the better!
Agatha Christie loved Miss Marple but came to hate Poirot.
Horrid, prissy little man!
Which is why I find Miss Marple tiresome, but can never get enough of David Suchet's Poirot.