@c0up It was strange because some of my blogs had the import RSS option and others didn’t. Customer support wrote back to me very quickly. Here’s what they had to say:

Hi Karma,

In order to conserve our resources, Tumblr is no longer supporting feed imports on blogs that have not already imported feeds in the past. We deeply regret any inconvenience that this may cause. But, this change will allow us to focus our resources and energy on other useful Tumblr features.

Sorry we can’t be more help,

Renee