This issue was fixed (for the time being) in version 2.56 released on October 22nd - but the overall situation is still the same.
As of October 20 the RunKeeper integration is down again.
This time Asics blocked a different, undocumented API call used by RunGap.
It is a little ironic that this also broke logins from their own RunKeeper app on Android. Because of this, I was hoping that they would remove the block again after discovering this - but apparently this is not a priority or no one is installing RunKeeper on Android devices (?).
So, once again I am trying to work around this - but it may take some time.
You can read more about the sad RunKeeper situation here.
Thanks for your patience.