Not impossible, but unusual.Are you sure the pivot for the pedal is clean and lubricated? If neglected that can get so stiff the return spring isn't sufficient to pull the lever back up.
No direct experience with an MC failure, but I'd say it was highly unlikely an MC will stick. It's more likely to leak, leading to less power to the brake. More likely is it being held by the pedal mechanism, or perhaps you've just been unlucky with the calipers sticking.Are you sure you've not been accidently resting on the pedal when riding? How long has the new caliper been on, and how often have you given it a clean (general clean, when it's on the bike - not a service/clean).