Make sure all bolts are tight, especially the bolt that attaches aluminum tailwheel casting to spring. Note that it is common for the aluminum of the casting to "flow" under the washer, with the washer bending and dishing in - this loosens things up. The fix is to use a high strength washer, of as large an OD as will fit, to spread the load over a wider area of the casting. I made my washer on the lathe.
It may be necessary to disassemble tailwheel, clean and re-lube, and check that there are 5 springs present.
Tailwheel springs should not have too much slack.
I've gotten in the habit of keeping the tailwheel off the ground until slowed way down. Procedure I use is: Land tailwheel low then stick forward to plant mains. If stopping distance isn't critical, leave flaps down. Allow to slow as much as possible, put tailwheel down gently while there is still enough energy remaining for elevator to prevent it falling (i.e. If you are braking aggressively and slow it way down with the tail up, if you get off the brakes abruptly, the tail will tend to fall). The key is to balance remaining energy so as to keep the tail off the ground until ship is as slowed as much as possible, but put the tail down gently with elevator and/or getting off the brakes while enough energy remains to do so gently and elegantly (no bouncing the tailwheel allowed) . . . and no shimmy.
bumper
