Hello Pedro and Jobu,
I will leave this question open since CRO and shopping cart abandonment rate tips are sure to generate a variety of opinions and experiences. Here are my thoughts on it...
1. If you have any up-sells, which are very common with digital products, put them after the order submission so you get the main order before potentially annoying them away with upsells.
The logistics of this depends on how your eCommerce system works and I have no experience with Shopify in this regard.
2. If any of the abandoned cart shoppers have given you an email address you can contact them with a follow-up email reminding them that they have items left in their cart. It could be good to combine this with an offer that you plan to give to everyone:
"This is just a friendly reminder that you have 5 items in your cart on mywebsite.com. Check out before Friday to receive our 10% off Spring Savings offer on your entire order!"
3. Consider using a "Usability Testing" service. Most of them will include screencasts as the tester goes through the site and comments what they find useful, annoying, odd, etc... You can ask them to pay specific attention to the checkout process. Who knows what they'll find, but some common items are: Asking for too much information, Lack of security badges / trust symbols, browser-bases security warning pop-ups, slow loading pages, change of domain...
4. A certain level of shopping cart and checkout abandonment is normal. For example, I almost always have some stuff left over in my Amazon cart for later purchase. Adding Wishlists (which Amazon has done) could help, but will not completely eliminate the issue. Some people are just comparison shopping. Your numbers do seem rather high though.
5. Consider retargeting ads to those who have abandoned their cart. Seeing your site as they browse the web can bring them back to their purchase, and should have much better conversion rates than other types of advertising online.
7. Sticker Shock is a big issue if you don't show them their running total as they shop. The upper-right corner is a good spot for this. Be sure to include the shipping cost if possible. Finding out the shipping costs (if that is even an issue since you have digital products) during checkout is a big cause of abandonment.
8. Always provide a means to contact customer support throughout the entire process. They may have a last-minute question before placing the order. Being unable to find the contact information easily is a sure way to lose their trust.
Good luck!