Yosemite keeps asking to install Java runtime, while it's installed

Install the SDK instead of the JRE.

I had a similar issue: I installed the JRE and ran the webpage-based test that said I installed successfully. But my java-based app wouldn't run, and running java -version in the console said Java was not installed. On a whim I decided to install the full SDK and now it all works.

Apple has a page here where you can download an updated version of Java.

More information can be found from this oracle help page:

https://www.java.com/en/download/faq/java_mac.xml#yosemitejava

This is a known issue on Yosemite and El Capitan, when some software requires the deprecated version of Java 6 shipped with earlier versions of OS X.

Information from Apple about this issue: https://support.apple.com/kb/DL1572

Oracle has a page about the issue here: https://www.java.com/en/download/faq/yosemite_java.xml

You need to download and install the legacy Java 6 provided by apple, from the first link.