MSN LCL CTLR WAS LATE IN CORRECTING ERROR BY STUDENT DURING MULTIPLE RWY DEPS RESULTING IN SEPARATION LOSS BETWEEN RWY 21 DEP AND RWY 18 ARR.

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I WAS INSTRUCTING ANOTHER CTLR ON LCL CTL POS. RWYS 18 AND 21 WERE IN USE. ACR Y HAD LANDED RWY 21 AND WAS HOLDING SHORT OF RWY 18 BECAUSE OF LNDG TFC. ACFT X WAS IN POS ON RWY 21 ALSO WAITING FOR TFC TO LAND RWY 18. AS SOON AS TFC CLRED THE INTXN OF RWY 21 ON RWY 18; MY TRAINEE KEYED HIS MIKE TO MAKE A XMISSION. WHAT I EXPECTED TO HEAR MY TRAINEE SAY WAS TO HAVE ACR Y CROSS RWY 18. WHAT MY TRAINEE SAID INSTEAD WAS TO CLR ACFT X FOR TKOF WITHOUT DELAY BECAUSE OF ADDITIONAL TFC INBOUND TO RWY 21. I IMMEDIATELY INSTRUCTED MY TRAINEE TO CANCEL THE TKOF CLRNC WHICH HE DID. UNFORTUNATELY; THE XMISSIONS WAS EITHER BLOCKED OR NOT RECEIVED BECAUSE ACFT X CONTINUED HIS TKOF ROLL AND DEPARTED. THERE IS A LOT OF TRAINING BEING DONE AT MSN RIGHT NOW. THERE ARE 9 TRAINEES WITH 17 CPC'S SO TRAINING OCCURS REGULARLY. MY TRAINEE HAS QUITE A FEW HRS AND MAKES THE CORRECT DECISIONS MOST OF THE TIME. WHEN THIS INCIDENT HAPPENED I WAS LETTING THE SITUATION DEVELOP INTO SOMETHING THAT LEFT LITTLE ROOM FOR ERROR. AT THIS POINT IN MY TRAINEE'S TRAINING I FELT THAT WAS THE CORRECT THING TO DO. UNFORTUNATELY AN ERROR DID OCCUR. FOR TRAINING; TRUST MUST BE EARNED BY THE TRAINEE AND I FELT COMFORTABLE IN THE SITUATION THAT THE TRAINEE WAS RUNNING. UNFORTUNATELY; WHEN 2 PEOPLE ARE TALKING ON THE SAME FREQ; THE XMISSION DOES NOT GET UNDERSTOOD BY ANYONE. I DON'T KNOW WHAT THE FIX IS FOR THAT. WHAT WOULD HAVE HELPED A FEW YRS AGO WOULD HAVE BEEN TO HAVE MORE TRAINEES TRAINING AT THAT TIME INSTEAD OF HAVING SO MANY NOW. THE FAA AND THEIR STAFFING PLAN IS COMING UP TOO LITTLE; TOO LATE.