Ecommerce business: Do you think that I should double the marketing investment in order to double the revenue that an e-commerce store generates?

invest according to the needs not on the whim that by doubling it you can double your business that way 

There are some factors coming into play here that you need to be aware of. With your current investment what is your ROI? is it break even, lower or higher? You need to do analyze the traffic that you get. Since you have used the word double I am assuming that you are already investing in your e-commerce business. If your ROI is good and there is still a lot of traffic that can be potentially converted into sales then you can up your budget, now I have no idea what your budget it but you do not need to double it but rather increase it a bit and see if that improves things, keep tweaking it every now and then.

You should first check whether existing Marketing Plans are performing or not. Doubling without checking would not gauranttee an increase in revenue.

Before moving ahead with increased budget check for the following :-

1.) Check the analytics of the website to determine the demography of traffic

2.) Whether changes in the e-commerce landing pages or website is to be made

3.) Target Audience