I think that's a problem with digital games, what happens if the Steam, Origin, Uplay etc servers shut down will we have access to the games that we purchased? Or do we own them until the servers die. It's a fundamental flaw with the digital market.
Speaking specifically for Steam, part of the terms you automatically agree to, and of which existence they remind you of every time, when you purchase a game, specifically states that your ownership of the game only extends for the lifetime of the service. When Steampowered is canned, your ownership over the games purchased through that service dies along with it.
Edit:
Steam Subscriber AgreementEdit2: This specific section in the agreement is what I'm referring to:
10. TERM AND TERMINATION
C. Termination by Valve
Valve may cancel your Account or any particular Subscription(s) at any time in the event that (a) Valve ceases providing such Subscriptions to similarly situated Subscribers generally, or ( b ) you breach any terms of this Agreement (including any Subscription Terms or Rules of Use). In the event that your Account or a particular Subscription is terminated or cancelled by Valve for a violation of this Agreement or improper or illegal activity, no refund, including of any Subscription fees or of any unused funds in your Steam Wallet, will be granted.