Sticky cases are a sign of excess pressure. When I started loading 325 gr WFNs in my .44, I ran into this when I discovered that some bullets where significantly heavier than 325 grs. Some cases also might be thicker/heavier, particularly if you use mixed brass, resulting in slightly less powder volume, which also can result in increasde pressure. If you have a heavy bullet in a case with less volume, high pressure will be the result. If you're shooting cast, be sure to check the bullet weight, and reduce the charge slightly when bullet weight exceeds the mean weight. Your powder charge should be such that you can shoot the heaviest bullet in the smallest case without it sticking.
If you're throwing powder charges, check the weight you throw every 10th round or so to ensure your powder measure hasn't gone out of adjustment. Keep the reservoir close to full to minimize the head pressure, which in turn minimizes variations in charge weights. I was loading 1000 rounds of .38 Special for a club shoot once, and my thrower went out of adjustment, it was the slide adjustment type rather than micrometer adjustment. When I realized I was throwing 7 grs of powder rather than 4.5, I had not idea when the problem occurred, so I went out and bought 1000 rounds (I had little spare brass) and kept those reloads for use in my .357. Needless to say, I didn't make much on that deal.
Don't pry the brass out of your DA cylinder. Simply use a wood or brass drift that will fit past the chamber throat and into the fired case, then gently tap it out. If the cases are gummy with lube, that might cause them to stick as well, so wipe them down prior to shooting them.