So the power source is not the problem. Since it is on 700mA
Your power source is capable of 700mA, but is the regulator? The linear regulator could be overheating. I believe the Bluetooth module was intended to be used by the 5V version (especially if powered with an unregulated supply.)
If the Bluetooth draws 150mA, this means the on-board regulator is dissipating the following.
5V Model: 7.2V - 5V = 2.2V * 150mA = 330mW
3V3 Model: 7.2V - 3.3V = 3.9V * 150mA = 585mW
Keep in mind that these regulators do not have a heat sink, other than the PCB itself. So if you are using a 3V3 version of the Arduino Pro, it is very likely the regulator is thermally shutting down. It may even be possible for the 5V to be shutting down because of the relatively high input voltage.
Are you using a 3V3 or 5V Pro?