This time I didn't have much white sugar, so I added half cup brown and half cup white sugar to my carrot cake.  I observed that the cake crumbled on the top with large cracks, and took very long time to cook as compared to previous same cake in which I had used just white sugar.  The change that I did to the cake was to add half cup brown sugar. The taste was same as before.  Can brown sugar be the culprit here? 
I usually add vegetable shortening to my frosting recipe so that it doesn't melt easily. I live in India and it's hot in here for crying out loud. Another helpful tip is to add 2 tsp Meringue powder to your each icing batch, that tends to avoid the weepy icing.  Hope this helps.   (Source: Years of commercial bakery experience and my fair lot of sad weepy but delicious cupcakes) 