I assume that you want to replicate insertions from the Publisher, but keep them on the Subscriber for longer; so when they are deleted from the Publisher the Subscriber still has them?

I don't have a development environment in front of me right now, but you can replicate just the inserts to a subscriber database. Using this method you can keep data on the Subscriber for a different length of time than the Publisher.

The command for adding articles (sp_addarticle) has parameters (if I recall correctly) for @ins_cmd (the insert process), @del_cmd(for the deletion process) and @upd_cmd(for the update process).

If you have 'NONE' set for @del_cmd and @upd_cmd then the replication will only process Inserts; Deletions and Updates won't have any impact on the Subscriber.

You can achieve this by scripting the Add Article or within the Wizard there is a 'Statement Delivery' section within the 'Article Properties' option when selecting the Articles. 'Update Delivery format' can be set to 'Do Not replicate' and 'Delete delivery format' set to 'Do not Replicate'.