This may be related to the bug other people have reported about the game reverting to a previous state -
I'm playing career mode on the PS4. With some contracts - so far, I've mainly had this problem with equipment tests for the R&D vendor - I will complete the test and satisfy all parameters, get the green text that says the contract was completed, end the mission, recover the craft, go back to mission control - and there's the same contract in my 'active' list, waiting to be completed.
This has happened repeatedly with parachutes and solid fuel boosters tests for the R&D vendor. If you need a gameplay video I can probably make one, since it seems to happen consistently.
I haven't diligently tracked what's happening to my funds and reputation balances (or KSC local time) through all this, so I can't tell you if the entire game is simply reverting to an earlier state or not. But I can't imagine why it would happen with equipment test contracts and not with, say, orbital rescues which don't seem to have the same issue.
EDIT: Shutting the PS4 down completely and restarting it apparently fixed the problem with one of the contracts - when I flew the same "haul the parachute up to 5-8k meters" mission again, it registered as completed.