Hi there.
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Start with checking store's speed and mobile friendliness in Google site insight.
Do you have Google analytics setup with defined goals? That will show you where visitors are leaving the site.
Also, almost any livechat is very useful to see what visitors are doing and push chats on them to get a live feedback.
There are few services which will give you a heat map and movie like recording of each visitor in your store.
Above will give you some ideas on what has to be fixed to get a conversion up.