This question is based on the assumption that the reason a prayer wouldn't be accepted is because it isn't heard. However, Hashem hears it all. While you may not be Zoche for that request to be answered, you might be Zoche for this request to be answered. The Gemara in Sanhedrin 44b specifically says that a person should always Daven that there be no obstacles in acceptance of his Teffila. The Maharal in Nesiv Hoavodah 12 explains this a bit.
The ערבי נחל (I think) and other Chassidishe Sefarim explain that when we Daven we are clearing a clogged pipe, so to speak, because of some Kitrug. When we pray, we are opening up these channels, by means of our realization of how we are completely dependent on Hashem. See מהר"ל נתיב העבודה
Therefore, even if a Tefilla won't do the job in its specific area, we ask a separate request to accept our Tefilla. If this one does its job it will help for the other in retrospect. Think of how you can run a debugging program that will fix the computer it is running on.
We find this in the Pasuk in Shemos where it says Hashem heard their cries, remembered the Avos, saw their plight and knew. Later there is a different order because of the context. But we see that there are certain Zechusim needed for the acceptance of a prayer. We can pray for that, too.