This depends entirely your horizon for what you consider a missed mate. Is there any upper bounds on the number of moves required? Would you consider a "mate in 53" to be a missed mate, even if no one, human or computer, had the computational power to actually find such a mate (but maybe in 100 years a computer could show a forced mating sequence from that position)?
Assuming that you would consider a missed "mate in 53" to be a missed mate, then the answer is that no one can give you a precise number, for the simple reason that no one can determine which situations contain such a mate. There does, however, exist a theoretical answer: the number of missed mates by a player in any game is precisely the number of instances in which that player had a winning position at one time but later the position became drawn or lost. The key insight is that a forced mate exists if and only if one of the players has a won position, even if the horizon for that forced mate is so far out as to be effectively impossible to compute.
You could probably get a reasonable estimate for the number of missed mates in a given game by running the game through a good chess engine and setting an appropriate cutoff evaluation, where any evaluation above that score is considered a won position for that player and any evaluation below that score is considered a draw or a loss. Since a pawn is generally considered enough to win, a score like 1.0 or 1.1 might be a reasonable choice. The number of missed mates would then be the number of times the computer evaluation crossed that cutoff line from high to low -- e.g., if the evaluation was 1.4 one move and .6 the next, quite probably the player moved from a won position to a drawn position, missing a theoretical forced mate. The downside to this method is that it is sensitive to the cutoff evaluation chosen, the engine accuracy, and the engine stability. Possible very sensitive, as it is quite possible to imagine a situation where a sequence of player moves or engine analysis at different depths fluctuate frequently over the chosen value in a narrow range, leading to large uncertainty as to whether the current move does in fact represent a change from won to drawn or vice-versa. Similarly it is quite possible that one engine evaluates a position as above the cutoff while a different engine deems it below.
A precise answer is clearly impossible, but if people are interested and time permits, I might try running a grandmaster game or two through my engine and see what results come out.