By default logic apps will be set to trigger every 60 minutes which, if you are not aware, may lead you to thinking that your logic app isn’t working at all!
As Logic Apps are preview there are some features that are not available through the designer yet, but you can do a lot through the Code view.
In this instance you can set the frequency to Second, Minute, Hour, Day, Week, Month or Year. For a frequency of every minute it is required to be on a standard service plan or better. If your service plan doesn’t allow the frequency you will get an error as soon as you try and save the logic app. Here’s what I set to have it run every minute.
More information can be found at https://msdn.microsoft.com/en-us/library/azure/dn948511.aspx.