Flour types and their effects in levain
You can feed your starter with whatever flour you have, keeping in mind the following things:

1) If you want to change flour type you should start with an active, healthy culture (don't start with one that is dormant or low activity). I would feed it at room temperature using the normal flour for a few days and make sure it is robust and active. Your new flour will have different yeast and bacteria strains which will compete with those in your current starter, so expect there to be a period of lower activity while things adjust to your new food. If the starter is not healthy and active enough to begin you could end up with problems like you did. 

2) You may need to feed it more often, and you should keep it at room temperature to give it the best chance of a healthy transition.  

3) this will change the flavor profile of the bread. The extent to which this happens depends on the type of bread and method you're using. 

4) some flours make more robust starters than others. Also, starters with some flours need to be fed more or less often than others. You need to judge the activity of the starter.