A Tumblr blog may not be the best solution but spending that many resources on a blog (especially one not featured in the main navigation) is usually out of the question for most startups.

For most startups the amount of time invested for a custom Jekyll setup and a downtime script could be replaced with a new feature or a better product/home page.

I think its important for startups not to spend too much time blogging unless they feel it will provide them some decent traffic and strongly support the product/company. Make the product better first. If your blog host (Tumblr) isn't stable enough, wordpress it and be done with it.