I was told a few times by Technicians, (before Telkom screwed me over royally with my ADSL), that rainy weather could often cause certain vital parts of the line to become wet. Often when it dries up the issue goes away, but you can sometimes get a Technician to fix the problem properly by sealing it against water.
A loose connection could also be an issue. It can flare up in stormy weather due to the wind. Then like someone else also mentioned, the static in the air from thunderstorms can cause problems.
Also I read someone leaves their modem plugged in even during heavy lightning. All I can say is - Maaaan you are lucky!! I have lost 3 modems to lightning.