A typical with 94s and 71s...Try letting the hammer all the way down then bringing it back to half cock and see is the fixes the problem, it usually does....If not you need a new hammer or sear..

My M71 trigger falls from the half cocked position when the trigger is pulled. What can I do to fix it.

Take it to a competent gunsmith.
Frank

Ya J Zola
Your trigger has two notches.One just square for the for the sear to sit in,the other grooved to actually hold the sear.The little outter tab on the groove must be snapped off or burred on yours.GUNSMITH time for SURE

Can the original trigger be repaired? Any ideas about a good gunsmith for this job.

Old '71 or new '71? With the old ones it is the hammer that has to be fixed. I don't know anything about the Brownings. You may actually be able to find a replacement hammer (Gun Parts Corp.?). Turnbull works on these so he could probably repair yours.
C.G.B.