^^^ FWIW my wife had a similar problem when applying for her CHL (now LTC), but TX apparently has a policy where they essentially call it good after a certain number of tries, 3 IIRC.
That said, it was still irritating because it delayed the process by 2-3 weeks each time, because they would send her a letter, and then she would have to make another fingerprinting appointment.
(FWIW TX does not require that the prints be made by a LE agency. Hers were done by private companies.)