I actually do both!
I leave the blade in my three piece razors until I decide they are toast. I then scrub the razor clean, dry and toss the blade.
I remove the blade after every shave with my TTO razors. I rinse and dry the razor then replace the blade. I do this mostly because of the condition of the "chamber" of every TTO I've looked at. Seems that's where all the nastiness likes to live.
I leave the blade in my three piece razors until I decide they are toast. I then scrub the razor clean, dry and toss the blade.
I remove the blade after every shave with my TTO razors. I rinse and dry the razor then replace the blade. I do this mostly because of the condition of the "chamber" of every TTO I've looked at. Seems that's where all the nastiness likes to live.