We have got an activity chain through different tasks and processes which fails

If you miss this link, Appian is already pointed out this at : forum.appian.com/.../Configuring_Activity-Chaining.html
So to trace the exact reason, you need to check your process model against to all mentioned points in the above link. As per my understanding this will give you more knowledge to try alternatives also

Right, there are several reasons for activity chain breaking, check log4j if you could increase logging to debug.

For activity chain I recommend to follow best practices very closely as it impacts the over system performance.

@mohamedb Added to other's suggestions, I would like to suggest you to go through the instance's Process details ('Process Nodes' in particular). This will give you a high level idea about the time consuming operations. This serves your purpose incase if the operations (or nodes) being carried out in the process are heavier in terms of size and time. Actually this is one of the ways we used to opt for, to find out time consuming operations which thereby leads to chain breakage.

One more possibility could be exceeding the max nodes (generally configured at 50) in the process models between two user input nodes.. Please verify that as well. Thanks

In addition, sometimes if you chain correctly, and everything runs correctly, and it still breaks, it may be because the nodes are taking too long. If that's the case, it may be in your interest to go back and reduce any redundancy, change some subproceases to run asynchronously to allow the main process the proceed quickly, or find ways to reduce the number of nodes within the chained process

Thank you guys! That helps.