Trial lawyers should object until the court denies them relief.
Let's look at an example. Your adversary mentions a prior conviction of your client that's already been found to be too old to be mentioned and irrelevant. First, you object-- "Your Honor, I object, violates Evidence Rule 609(b)." (As a practical matter, you need to choose your one best objection. Also the rule number is a nice touch. The Court of Criminal Appeals can't complain you were vague about your objection.) Let's say the judge sustains your objection. YOU ARE NOT DONE. Move for an instruction to the jury to disregard the statement. "Your Honor, I move for an instruction to disregard the statement." Let's say the judge grants your motion and gives the instruction. YOU ARE NOT DONE. You should move for a mistrial; "Your Honor, I move for a mistrial." The judge will not likely grant this. If the judge does, the trial is over, and will have to start again. The judge will likely deny the motion, but if the judge should have granted the mistrial, you will have preserved error.
What happens if you stop too early? If the judge grants you everything you ask for, you don't get any error preserved. The appellate court won't--can't-- overrule the trial judge because the trial judge did everything you wanted.
Don't let the judge's giving you the fish eye or telling you to move along make you hasty. Keep going till the judge denies you relief.