The fact you no longer have the item you bought from the shop weakens your case. Also, as they were not involved in the replacements, there was no reset in their obligations to you with those replacements.
You should be aware that you do not automatically have an entitlement to a refund, and the shop/ manufacturer are entitled to repair or replace the item. However, any such repairs are expected to last so you may have a case, but the nature of the item and use will have a bearing on what is considered reasonable.