If by "broken down" you mean you've removed the trigger pin, and now the drawbar lifts upward (whether the trigger is pulled or not) ... that's one of the reasons there's a trigger pin.
The drawbar plunger spring is pushing against the head of the drawbar assembly, and unless the trigger pin is in place it can shift & lift due to spring tension and clearance in the channel in which the drawbar is located and moves.
The trigger play spring can be replaced easily enough by the company (or a gunsmith familiar with S&W pistols).
The gun will run without it, but the trigger will have some "slop" to it in SA mode. Probably not something most owners/users would notice when just shooting the guns, though. I once had an older style trigger play spring break off and vacate the gun at some unknown point during a 2-day, 800+ round practice period. Since I was doing defensive training drills, and not slow-fire target shooting, I never noticed any difference in the SA trigger mode.
FWIW, the CHP finally removed the trigger play springs from their older 4006's, and ordered their new 4006TSW's with drawbars that didn't even have a trigger play spring.
It's not a terribly difficult repair, but it does require knowing how to fully disassemble the frame, and then reassemble it. Also, during reassembly it's important to know how to push the drawbar back into position, getting the drawbar plunger properly located within the recessed notch in the head of the drawbar (and keeping it there while holding the drawbar positioned for installation of the trigger pin) ... and being able to do so without letting the drawbar plunger spring tension lift the head of the drawbar as it's being installed, causing the new trigger play spring to be caught against the frame and damaged. It can be a 3-handed bit of multi-tasking, requiring you to hold your mouth just right, until you've done it several times.
The old spring TP spring base is easily punched out of the rivet hole with a 1/16th inch pin punch, but the replacement spring has to be kept firmly seated against the drawbar while the soft rivet is carefully flattened. (This is where some new armorers get side-tracked and fail to install the new TP spring properly.)
The whole procedure only requires a 1/16th inch pin punch, a pillar file with a safety edge (which is used as a work surface when the file is secured in the vise jaws at one point), a small vise and a small ball peen hammer.
As with most simple mechanical procedures, though, it's knowing how to do it that's the trick.