I tend to agree with Tony. Disassembly so that you can look at the gun may prove very helpful. Who knows, you may even see something that is hitting, rubbing or whatever before you do anything else. Just look at everything carefully and clean and lube. Seems the grips on Bersa 380's give some problems moreso than a lot of other pistols. If they're too tight, they rub and cause problems. Might cause clicking, I don't know. Dry fire without the grips on may also give you some answers.
So do a careful inspection and cleaning. Lube it and make sure everything is free. Grips not too tight and go shoot that baby! One question: why drop the hammer after initial loading? Don't want the first shot to be SA for some reason? Don't know that that has anything to do with it, more curious is all. Good luck with your project!