Language development changes in speed with the linguistic landscape. Persian saw its fastest changing in the 8th century during the Ummayad conquest, when Arabic became the dominant language of the ruling class.

Similarly, English saw its fastest changing in the 12th century during the Norman conquest, when French became the dominant language of the ruling class.

In both cases, most of the core vocabulary and grammar survived, but with enough influence and new words that it is hard for speakers after the change to understand writings before the change.

My understanding from Persian friends is that Rumi is about as understandable to modern Persian speakers as his contemporary, Chaucer, is to modern English speakers.

Whan that Aprille with his shours soothe

The droughte of March hath perced to the roote

And bathed evry vein in switch liquour

Of which vertu engendyred is the flour...