How many times can they postpone my brother's trial?

It depends on why it was postponed. If they do it without good cause, then they could end up having the case dismissed. This would be with out prejudice. (That means they could recharge him at any time.)

It is discretionary with the Judge in charge of your brother's case. All defendants have an absolute right to a speedy trial. However, the Court may grant adjournments of the trial proceedings, for good cause shown, either on behalf of the prosecution or the defense. If all the delays are not the fault of the defense, upon proper motion and argument, the case has the possibility of being dismissed. This is not to say the the charges can again be re-instated against your brother at a later time, as jeopardy has not yet attached.

Generally there is a rule that a trial must be commenced within 180 days if the accused is in jail. However, if is possible that has been waived. You should be seeking this information from your brother's attorney.

The Court has great discretion in scheduling trials. When the charge is murder the trial can be held years after the charge. But his Defense Attorney should file a Demand For A Speedy Trial.