For all practical purposes the answer is no. A felony warrant will stay open until they find you. Moreover, if you got arrested in another state they will likely hold you and begin extradition proceedings to bring you back to Texas in custody. Once you are in custody, your lawyer will be able to argue various issues like due diligence, etc.
The bottom line is that you will have to deal with this at some point. It is always beneficial to have a lawyer on board prior to "turning yourself in." Depending on the jurisdiction and prosecutor you may be able to accomplish some things ahead of time and reduce the chance of you going to jail (or the amount of time you spend there if you do).
Feel free to contact me if you wish to get started on this.
It doesn't ever "go away" unless the issuing agency recalls it, which is pretty unlikely to happen with a robbery. I imagine the only chance of the warrant getting recalled is for someone to realize, IF the DA's office hasn't gotten you indicted by that time, that the statute of limitations (five years) has run on the case and that you can no longer be charged with the crime. Whether that's even a possibility probably depends on things like agency procedural policies and whether you end up falling through the cracks, not on anything fo do with you or your specific case.