The more the grip is allowed to work under stress the more it responds and becomes stronger, usually at a very fast rate. A strong grip (including thumbs) is one of the most important survival tool given to human's and all the other primates. If the grip gives out too soon in a workout than some attention should be given to it. The more logical approach would be to just hold (static) a BB with 50 to 100lbs over your normal DL for a count of 10-15 seconds or so from a set pin position in a power rack, lifting boxes, supports, etc.. This not only can improve the grip but also the DL it's self. Hanging from a chinning bar with extra weight attached can help greatly with the power and endurance of the grip. One arm DL's and chins are also a outstanding way of improving the grip and rather quickly. Can also grip and hang from a over head rafter or beam for strength, which will place extra demands on the thumbs. Though BB\DB wrist and finger curls do have their place, a heavy static hold workout would always be first.
Might try these above mentioned exercises after a normal workout, with 3 sets of 10-15 second DL or chinning bar holds. Good Luck.