This issue is discussed here.
Summary: Magazine subscriptions to Jewish-owned publications are forbidden only where the discount is explicitly or obviously linked to the advance payment. In this case, the discount is usually linked to other factors, so most poskim permit it.
A little research online shows that the primary reasons that magazine publishers offer discounted (often severely discounted) prices for subscription is to raise advertising revenue (as advertisers pay more to be featured in magazines with more subscribers), and to be guaranteed the purchase for the whole year. This would then be permitted for Jewish publications.
However, if the subscription discount is advertised in a way that highlights the fact that the discount is for advance payment (e.g. "Subscription price is contingent on prepayment in full," or, "Pay for a year and save 45%") this would be problematic.
In the discussion here (note 43) though, an interesting problem is brought up:
If the price of the periodical increases during the subscription period, the subscribers could not be indemnified from the increase. In this case, a new subscriber who joins after the price increase is charged a higher price than the person who subscribed earlier. All of the outside motivations...apply to both subscribers. The only reason that those who subscribed earlier are protected from the increase is because they advanced funds at an earlier time. This benefit is prohibited.
The practical solution given there is that the publisher should offer the subscriber the option of paying the publisher itself or to place the money in escrow to be withdrawn by the publisher at the appropriate time. This eliminates the possibility that the discount is motivated by the advance payment. [It is also recommended that a heter iska klali be used.]