What are the consequences of indefinite postponement on each of the following types of systems i.e.Batch processing?

The answer depends upon if the batch is itself part of a larger transaction 'batch' - If it is the result could have a negative or cause incorrect data to be generated.

(Transactional Processing is where the 'whole' thing (all items as a set) much complete successfully or the whole transaction is considered failed. In the above question, delaying any one particular batch in this case will cause eventual if not immediate transactional failure.)