If a deal isn't struck viewers are not going to move to another platform just to continue receiving them, especially if they look at Discovery's recent negotiations meaning they're just as likely to pull the same tactic there in the near future too. Some might go to the Eurosport Player, but that is a very poorly supported service at the moment which doesn't think much beyond casting. If they're serious about Eurosport they need to get the player on Now TV and other platforms, and their current stance makes that look unlikely.
I know it's one thing to say something and another to do it, but I have two twitter searches in Tweetdeck, one for "Eurosport" and one for "Discovery Sky" and literally every few seconds there is a new tweet from someone saying they'll leave Sky or asking where they can find Eurosport or Discovery Channel if it goes.
Sports fans are going to seek out the coverage, whether that's on another provider such as Virgin or TV Player Plus, or through betting or illegal streaming sites. The grand slams - while only 6 weeks of Eurosport's content - are the most important events for tennis fans, and likely to bring in bigger audiences than the ATP Masters on Sky or WTA tour on BT Sport. Eurosport have sensibly retained some of the rights to the smaller tennis tournaments in between the grand slams to hold interest.
The more niche the sport, the more likely a fan is going to have sought out that specific coverage, whether it be superbikes or biathlon or ice skating, which probably isn't going to be available elsewhere. It will be one of the biggest reasons for subscribing to a Sky package. Sky's alternative offering that they put on their website is frankly laughable and patronising and shows they don't care for fans of anything other than football.
The WTA scored an own goal when it pulled out of the Tennis TV streaming service last year without any equivalent to replace it - which fans would have been happy to join. While I imagine the rights holders such as BT Sport might have seen a small increase in subscriptions due to this, it was clear from twitter that many fans, particularly in the US, moved towards the dodgy streams (
more).