I have seen operators let the chain get slack, only to let the carriage bang once the clamp is released. A properly charged accumulator solved the problem.

If you don't correct the situation, your hoist cyl packings will also begin to leak. It wasn't until this stage did the customer allow me to install the accumulator

I have seen some clamp truck operators that continue to hold the lowering lever forward even after the load is resting on another roll, or where ever they are putting it, causing the lift cylinder to continue to go down and slacking the chains. Then they open the clamp and bang, the carriage/clamp assembly drops, which must put stress on the chains.

One thing that might be contributing to chain breakage is if the chains go slack when lowering the rollclamp and then catching on another roll or something then dropping and the chains taking the brunt of the stress

been dealing with lifttrucks for over 30yrs
never have seen any widespread issues with liftchains breaking except only in an operator abuse situation
specifically in your case with the paperroll clamp on that big truck?
the truck being a 100 series its rated at about 10,000 capacity normally, with the paperroll clamp i'm sure that was downgraded to about 8,000 or there about?
you have to take that into consideration plus how the operator is trying to handle his loads, in alot of cases when i've done work at any type of factory that handles large paperrolls they do try and pickup multiple rolls at the same time, generally 2 at a time.
how much does each roll weigh?
does it exceed the truck capacity plate rating with 2 rolls?
is the operator trying to move around more than 2 rolls by taking the weight off of several stacked rolls and sliding them across the floor?

any of these situations can be contributing to chain breakage due to overloading the chain capacity.

if these trucks are low hour(fairly new) trucks this should not be happening for no unapparent reason.

just some things to ponder to help you on your quest to find out why.

good luck!

Have had turned pins and premature wear on the h5.50xm with PRC. The one I had did not have a hydra cushion/accumalator. Really needs a hydra-cushion to take out the shock.