It's clearly not possible with RoboSpice, and indeed, there is a good reason : it would be a very bad idea.
When your activity dies (onStop), Android wants to garbage collect its instance. And to do it, it should not be referenced by anything. That's why RS imposes that all listeners are removed. Typically listeners hold a reference to the activity (as inner classes) and the finest achievement of RS is to let the activity die properly and get garbage collected.
So, doing what you want would clearly lead to a memory leak, and moreover would lead to crashes most of the time: when an activity is not displayed anymore, you would like to update its UI ? Looks a bit ackward, doesn't it ?
Maybe the simplest would be to use a very limited cache, or just execute all your requests every time your activities enter in onStart.