My experience with quick links (SRAM and KMC) is all positive. I've been using chains with masterlinks for over 20 years and i cannot remember the last time I dropped a chain.
1. When you say drop your chain, is that the chain falls between the small chainring and frame?
2. When you put on the new chain, did you shorten it to match the length of the original chain?
3. I'm not sure I follow when you say you drop a chain and the quick link is there. Do you mean the link is positioned and laying on top of the bottom bracekt.