As speech-interfaces are getting richer and widespread, speech emotion recognition promises more attractive applications. In the continuous emotion recognition (CER) problem, tracking changes across affective states is an important and desired capability. Although CER studies widely use correlation metrics in evaluations, these metrics do not always capture all the high-intensity changes in the affective domain. In this paper, we define a novel affective burst detection problem to accurately capture high-intensity changes of the affective attributes. For this problem, we formulate a two-class classification approach to isolate affective burst regions over the affective state contour. The proposed classifier is a kernel-fusion dilated convolutional neural network (KFDCNN) architecture driven by speech spectral features to segment the affective attribute contour into idle and burst sections. Experimental evaluations are performed on the RECOLA and CreativeIT datasets. The proposed KFDCNN is observed to outperform baseline feedforward neural networks on both datasets.