Some half-cooked thoughts, not yet popped:
Issues make little sense online. Obviously, they’re necessary for print, but web readers — especially of a less news-driven publication — don’t think that way.
Some content is inexorably tied to a certain date. News and blog posts, in particular. (There’s context again.) But so much is timeless. Why force that content into an artificial issue framework on the web? The web is alive, constantly growing and changing. Does a web reader really care when, say, a great recipe was published?
Don’t think of the website as a repository for magazine stories and the stuff you had to cut from print. And certainly don’t think of the website as a “brand extension” and marketing tool to sell subscriptions. Your site is its own, complementary product. And, yes, you can make money online.
Consider a digital-first approach. Never stop producing stories for the web, and instead pull (and rework for print) the very best for a monthly magazine. Then add to the mag some new, context-appropriate content and you’ve got the kind of durable, evergreen product that magazine people love to hoard. Encourage your magazine readers to visit your website for more great stories, all month long. Macworld is a great example of this model.