I have the tissue-specific RNA-seq data and its corresponding ATAC-seq data. I first identify all the differentially expressed genes. Then using ATAC-seq data to check whether the promoter regions of those genes are differentially accessible. It turns out that only a small portion of differentially expressed genes'  promoter regions  are differentially accessible. I try to find explanations. One reason I can think about is that the data is not perfect so missed some signal. What could be other reasons in the biology perspective? 
We've never seen much in the way of correlation between chromatin openness at promoters and gene-expression changes. This is not totally unexpected. Studies of chromatin state find that chromatin in a promoter state is often the same across cell types (while enhancers tend to be more celltype specific). 

It becomes obvious that gene expression is not entirely controlled at the chromatin openness level when one thinks about plasmid based reporter assays of promoter function. If you put e.g. AP-1 transcription factoer dependent promoter in a plamsid reporter, and then compare AP-1 activated vs non-activated, you'll see a difference in expression, despite the fact that plasmids don't have chromatin. 