@Rob, thank you so much for your reply. How could I forget this info… That’s actually how repeaters are supposed to work! Huge miss on my side. Apologies for that.
Also, thank you so much for reminding me about it. Thanks to your message, I thought “well, then I must be doing something wrong somewhere”, and voilà, that was the case. First, the dataset that my repeater was using in the editor had a small number of elements per load (maybe this was being overwritten by my code), but anyway, I was also setting that same small number in a function where I was fetching the data from the CMS, and that was the main problem. Once I made the change to a bigger value, the problem was solved.
Thanks once again for the wake-up call!!! 
(By the way, when fetching data from the CMS, I am also using a function to get an info field from the registered user’s profile, should anyone who reads this be interested in something similar! You can check it here: Fetch and use site members' custom info fields )
Cheers!