14 -21 days is very fast. No argument there, though speed is not my thing even though I shake to carb.
Since you say it goes almost flat after a couple days, you're either not shaking it for long enough or at high enough pressure. Or a leak, even though as you say they are not usually difficult to track down. Regardless, something is going on there. I have kegs that are aging since last year that were only shaken to be carbed and I need to bleed the head pressure to pour a decent taste. They're only at cellar temp (60 or slightly less) so the carb and pressure would drop some if I put them in the fridge, but they certainly wouldn't be flat.