Problem on Chilli Plants
I've had this problem in the past when growing chillies of my own. Its natural for older leaves nearer the base of the stem to yellow but I've found that moving the plants to larger pots to prevent the roots becoming pot bound, reduce watering and also less feed (feed once every 2-3 weeks) prevented the stalks on the fruits yellowing and eventually dropping off.
Also by allowing the pots to dry now and then naturally reduces sciarid fly infestations as the larvae flourish in a continually damp environment.
Hope this helps, but if it continues please do get in touch again.