Heroku and AWS Timeout

I recently started testing an app hosted on Heroku with AWS as a backend. I'm commonly seeing relatively short requests timeout on a response on the Heroku side, which points the user to an error page, and then when looking at the application, it is clear that the request actually completed.

In general, the application is much slower than I expected. I'm using the micro database tier because I do not expect more than 60 users and not more than a handful at any given time. The demand is low.

It is practically unusable as is though. Simply going to a page where rails queries for a list of 100 records causes the page to time out. When run just with Heroku it was lightening fast. I need a larger database than Heroku can provide though.

Any suggestions?