Blog Subscriptions widget: Update follower count more often or offer force refresh

#### Steps to reproduce the issue
Add the Blog Subscriptions (Jetpack) widget to a site connected to social networks included in the subscriber count.

#### What I expected
The subscriber count to update as followers increased on social networks

#### What happened instead
The count does not increase for extended periods of time, but can be force refreshed using the "Clear Cache" button under the SUBSCRIPTION CACHE CHECK on the blog RC.

As a solution we could make this number update on its own more frequently or port the clear cache functionality that already exists to be user-facing within Jetpack.

Start by locating the Blog Subscriptions (Jetpack) widget and the SUBSCRIPTION CACHE CHECK flow, including its Clear Cache button on the blog RC. Compare the existing cache behavior with the requested automatic refresh or user-facing force-refresh options, then confirm the expected refresh policy and verify that subscriber counts update as intended.

Written by the indexing model from the issue text.