My WiFi is working fine, I've uninstalled and installed the app again three times and rebooted my device at least 5 times. Then I noticed that, along with Netflix, an task/app called BootDialog appeared in the task screen. The phone had never done that before, so I supposed that's part of the problem.
The failure happened after I updated the app, but I've tried it on other Android devices (my friends') and the app itself seems to be working just fine.