Association Rules Mining (ARM) is simply mining a given dataset for some kind of data that appear together frequently to form rules, while Distance-Based Association Rule Mining (DARM) is an enhanced Apriori algorithm that takes a distance between each pair of items within an item set into consideration. It is crucial to maintain such discovered rules from large datasets, this was the main idea behind Incremental Association Rules Mining (IARM), which has recently received much attention from the data mining researcher. In this paper we have added an incremental feature to the distance-enhanced association rule mining algorithm. The proposed algorithm updates a set of distance preserving frequent itemsets to reflect changes occurred to the original dataset. This update is done by making use of previous knowledge which was generated from a previous mining process on the original dataset and was kept for future updates. This knowledge includes the number of occurrences for each frequent itemset, in addition to the mean and standard deviation of distances within these itemsets occurrences. When the original dataset is changed, accessing the original dataset is needed to gather information of only the itemsets that were not previously frequent and have a potential to be currently frequent. Finally, the resulting algorithm has been implemented in Weka.