My plants shed their blooms when the weather is hot, 30+ for a few days in a row. I find most of the blooms set at about 20 - 28C. I don't shake my plants so to speak, but using 1 finger I tap the lower part of the stem to send vibrations to the flowers to get some pollen to move around. You could always get your finger stuck into them!
Make sure the flowers have pollen too. If conditions aren't perfect, you'll sometimes see flowers with absolutely no pollen on them. You can usually, quite quickly tell if a bloom is gonna set. If it starts to look pale green to yellow, its a matter of time til it drops. If it looks like its still growing, especially in thickness, then its a very high chance it will be set.
My plant outside, aji limon, was having a very hard time with weather and potential bacteria, flowers dropping everywhere. Since the weather cooled down and become stable, to my surprise, its now set about 6 pods!
You could also try GH bloom booster just to ensure the has a ready available source of nutes.
For me the most important factor I've noticed is temperature. Even if, nute wise, I give them little to nothing, they can set blooms but if the temps are too hot they come off. Not sure about cold. Were a few days off summer so cold does not exist. I will say though that its very likely the plant will shed blooms if its too cold. If a plant is cold or not receiving enough light, it will drop leaves or blooms to conserve energy. Maybe blooms drop when its hot because the plant is working over time to absorb moisture from the soil so it spits the flower and absorbs away.
