Hosting reply:
The JA Builder extension worked for 2 minutes and timed out again. I am afraid that the timeout limit cannot be increased more on our shared servers. It seems that JA Builder is broken or non-well optimized because 2 minutes should be enough for JA Builder to publish its data. Also note that certain PHP limits like max_execution_time, memory_limit, max_input_time, post_max_size etc. are set globally for the whole shared server and cannot be modified.
I would advise you or your developer to try optimizing the JA Builder extension and reduce its execution time. If such optimization is not possible and you really need to increase the account's timeout and PHP limits you should consider upgrading your account to our Cloud servers: