From: Mobile Pass Frequently Asked Questions (eurail.com)

Your mobile Pass is periodically checked against our system to ensure its validity and prevent fraud, which means that you need to be online at least once every 3 days.

 

We’ll send you a notification 24 hours before your 3 days are up so you can find an internet connection. If you are on a train, there may be on-board Wi-Fi that you can use. The app does not update in the background, so you’ll need to open the app when you find a connection so we can check your Pass.

 

If you haven’t been online in more than 3 days, your mobile Pass will be considered inactive and you will not be able to use your Pass until you connect to the internet and open the app. 

I rely on my old chromebook (right now also) and wifi in trains and/or stations or hotels and this has always got me through.