Same thing has been happening to me since the last day of the beta.
Mouse and keyboard work fine any other time and with any other game but I soon as I launch darktide and get to the Mourningstar the mouse and keyboard start locking up at random intervals, lasting anywhere from 1 - 5 seconds roughly.
Tried restarting computer, both wireless and wired mouse, etc… quite literally unplayable when you lose control multiple times per minute
having exact same issue. During the beta I didnt have any issues. First time I log in after its released I have the same delayed/stuck input for keyboard that everyone is having.
This seems to have been fixed now for me at least 
Edit: OK I lied it’s still there it just isn’t as bad, playable at least
Same issue as reported here: BUG: Input dropping.
Really annoying and unfortunately making the game unplayable.
So I have found a temporary fix, So it is ok for a bit but after a few missions it starts getting progressively worse. I just unplug the affected devices and plug (the USB socket) back in and it seems to alleviate the issue.
No clue why but 100% works for me.
I use a wireless razor keyboard (black widow v3 pro) and wireless corsair mouse.
I haven’t had any issues with the mouse as I do not have ICue running in the background HOWEVER, I noticed the lagged input/lockup with my keyboard. I thought it was the wireless 2.4ghz signal being interrupted but this behavior never shows in any other game.
When my lockups happen, my rgb on the keyboard spazzes out (for lack of a better term). Looking at razor help guidelines I suspect the Razor Synapse application software does not agree with Darktide.
I have since disabled synapse and have not encounter any lockups so far ((fingers crossed)