In "Marlowe on the Caroline Stage," Lucy Munro argues that by the time of the Caroline Period (1625 - 1642) there was already a developing tradition of classical English plays, hearkening back to the late Elizabethan/early Jacobean period. She further argues that the active publishing of these "modern classics" (contrasted with the classics of Greece and Rome) saw parallel revivals on the London stages. You may recall that Merry Devil was published in its fourth quarto in 1626 and then in its fifth in 1631, which may argue for its performances during the Caroline period.
I don't have a hard time believing that Merry Devil would have been revived, but that will come as little surprise. As Munro states, a direct parallel between a works life in print and its parallel life on the stage is hard to calculate, but it seems to make sense that, even if a precise calculus cannot be established, the general availability of a play in print argues for that plays general availability in performance. It's a simple fact of the modern theatre industry that more widely published plays get performed more often than less widely published ones, although it would likewise be difficult to create a precise calculus linking publications to performances.
What intrigues me most of all is her argument that, in attempting to create what is essentially a series of modern classics, Caroline actors invoked the authors of the Elizabethan and Jacobean periods, sometimes as characters within their play texts, and sometimes using a style of performance that was thought to more closely match the "original practices" of the earlier stage. Of course, as a student of The American Shakespeare Center, I am greatly intrigued by the idea that a pursuit of original practices in performance may date to the decades following Shakespeare's death.
A very close second is that this might help fill in the gap linking Merry Devil to Shakespeare in its sixth quarto (1655) by Mosley. Dr. Menzer has argued in our textual culture class that Heminges and Condell were creating the first English Author (in the modern sense) with their publication of the first folio of The Collected Works of William Shakespeare. If the figure of the "poet" (aka playwright) was regularly invoked on the stage for modern classics in revival, than Merry Devil comes with the serious disadvantage of not having a clear author. Mosley, knowing the play was a product of the King's Men, was of course trying to take advantage of the most revered English author in linking the play to Shakespeare, but his doing so might have had the practical purpose of linking a play that had been established as a modern classic to a writer of the period, the only one to whom he could plausibly attribute the play.