Yes, that's how the flopper should work. It should fall open with gravity and stay open, this is why the flopper should be mounted on the underside of the spear shaft. The spear penetrates the fish, then falls open, and most importantly stays open upon exiting the fish.
Thoroughly washing the gun in fresh water after every use is a must, especially inside the trigger mechanism if it has been exposed to sand.
Allow the gun to dry after washing, then store in a cool dark place to protect the rubbers from sun/UV exposure as this can reduce the life of the latex rubbers. For longer term storage, you can even remove the rubbers, put them in an airtight bag or container (vacuum sealing would be ideal), and place in the freezer.
Other than that, they don't need much care, inspect the rubbers for cracking and replace them when the cracking is more than 1/8" or 1-2mm deep. A little cracking will not make the rubber snap.
The Dyneema bridal should also be replaced when it is starting to frey. Check the shark fins tabs for any sharp edges. Lightly sanding or filing them to remove any sharp edges will greatly reduce wear on your bridal. I rig my guns with a double bridal which halves the wear yet again, and leaves me with a spare if one breaks. If you remove all the sharp edges from the tabs, the bridal should easily outlast the rubber.
Hope this helps,
SR.
