This has bugged me.
When text begins and ends with a quote mark because it’s part of text that includes a quote, Tumblr will discard the first and last quote marks.
This is the solution
Quotemark space quotemark text quotemark space quotemark
In other words, add quote marks at the start and end with a space between.
It will leave alone the second set as shown in this post.
Update: This quote problem only happens on the Tumblr itself. In the Dashboard, those who Follow will see two sets of quote marks now, with the space between. Yeesh.