Strengthening shampoo wont help. Hair loss is a scalp problem and has nothing to do with the strength of your hair.
Its true that you loose more hair during summer, especially when its really hot like it has been the past couple of weeks!!
Ive never had a problem with hair loss (as in big balls of hair) but I have noticed more coming out into my brush when I brush my hair lately! It really only seems to be like that on really hot days though.
If its an ongoing problem though, get onto Nioxin shampoo's and conditioners, and keep using them, make sure you arent alternating with any other products as it is an ongoing process to help reduce hair loss and kill the bacteria and nasties in the scalp
HTH